Search references for HOLOMORPHIC FUNCTIONAL-CALCULUS. Phrases containing HOLOMORPHIC FUNCTIONAL-CALCULUS
See searches and references containing HOLOMORPHIC FUNCTIONAL-CALCULUS!HOLOMORPHIC FUNCTIONAL-CALCULUS
Branch of functional analysis
In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function f of a
Holomorphic functional calculus
Holomorphic_functional_calculus
Theory allowing one to apply mathematical functions to mathematical operators
in these operators. Holomorphic functional calculus, which attempts to extend the techniques commonly used to study holomorphic functions f ( z ) {\displaystyle
Functional_calculus
Branch of functional analysis
Borel functional calculus is more general than the continuous functional calculus, and its focus is different than the holomorphic functional calculus. More
Borel_functional_calculus
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
See below for their application to compact operators, and in holomorphic functional calculus for a more general discussion. Comparing the two decompositions
Jordan_normal_form
Linear operator in mathematics
Borel functional calculus. The domain of a composition operator can be taken more narrowly, as some Banach space, often consisting of holomorphic functions:
Composition_operator
Banach algebras, in which only a holomorphic functional calculus exists. If one wants to extend the natural functional calculus for polynomials on the spectrum
Continuous functional calculus
Continuous_functional_calculus
Technique in mathematics
framework of holomorphic functional calculus. The resolvent captures the spectral properties of an operator in the analytic structure of the functional. Given
Resolvent_formalism
Representation theory of the symplectic group
symbol such that D – B4 is a smoothing operator. Using the holomorphic functional calculus it can be checked that D1/2 – B2 is a smoothing operator. The
Oscillator_representation
Mathematical operation
set of matrices. These properties are consequences of the holomorphic functional calculus applied to matrices. The existence and uniqueness of the principal
Square_root_of_a_matrix
equations. Hodge–Arakelov theory Holomorphic functional calculus a branch of functional calculus starting with holomorphic functions. Homological algebra
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Holomorphic functions in infinite dimensions
functions are important, for example, in constructing the holomorphic functional calculus for bounded linear operators. Definition. A function f : U
Infinite-dimensional holomorphy
Infinite-dimensional_holomorphy
Block diagonal matrix of Jordan blocks
vector spaces can be defined in a similar way according to the holomorphic functional calculus, where Banach space and Riemann surface theories play a fundamental
Jordan_matrix
Branch of mathematical analysis
this context the extension of holomorphic functions of a complex variable is developed as the holomorphic functional calculus. Hypercomplex analysis on Banach
Hypercomplex_analysis
Branch of mathematics
infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus studies
Calculus
Matrix decomposition
eigenvalues. A similar technique works more generally with the holomorphic functional calculus, using A − 1 = Q Λ − 1 Q − 1 {\displaystyle \mathbf {A} ^{-1}=\mathbf
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Formula in matrix theory
}{2}}(I-A)}=e^{-i{\frac {\pi }{2}}(I-A)}} . Adjugate matrix Holomorphic functional calculus Resolvent formalism / Roger A. Horn and Charles R. Johnson
Sylvester's_formula
Extension of the domain of an analytic function (mathematics)
theorem makes use of Hadamard's gap theorem. Mittag-Leffler star Holomorphic functional calculus Numerical analytic continuation Polya's shire theorem Kruskal
Analytic_continuation
Quantum operator for the sum of energies of a system
operators, a functional calculus is required. In the case of the exponential function, the continuous, or just the holomorphic functional calculus suffices
Hamiltonian (quantum mechanics)
Hamiltonian_(quantum_mechanics)
Bounded operators with sub-unit norm
_{n\geq 0}r^{n}a_{n}z^{n}}} is holomorphic on |z| < 1/r. In that case fr(T) is defined by the holomorphic functional calculus and f (T ) can be defined by
Contraction_(operator_theory)
Theory in functional analysis
As in the matrix case, this is a direct application of the holomorphic functional calculus. ▮ As in the matrix case, the above spectral properties lead
Spectral theory of compact operators
Spectral_theory_of_compact_operators
Mathematical operation on invertible matrices
operator is actually bounded. Using the tools of holomorphic functional calculus, given a holomorphic function f {\displaystyle f} defined on an open set
Logarithm_of_a_matrix
Type of vector space in math
notion of Euclidean space. It extends the methods of Euclidean geometry and calculus from the two-dimensional Euclidean plane and three-dimensional space to
Hilbert_space
Instantaneous rate of change (mathematics)
between the partial derivatives called the Cauchy–Riemann equations – see holomorphic functions. Another generalization concerns functions between differentiable
Derivative
Calculus of functions generalization
In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean
Calculus_on_Euclidean_space
Function that maps matrices to matrices
space, which can be seen as infinite matrices, leads to the holomorphic functional calculus. The above Taylor power series allows the scalar x {\displaystyle
Analytic_function_of_a_matrix
Branch of mathematics studying functions of a complex variable
the study of holomorphic functions that are the differentiable functions of a complex variable. By contrast with the real case, a holomorphic function is
Complex_analysis
Particular kind of algebraic structure
} the holomorphic functional calculus allows to define f ( x ) ∈ A {\displaystyle f(x)\in A} for any function f {\displaystyle f} holomorphic in a neighborhood
Banach_algebra
Mathematics of real numbers and real functions
that develops calculus rigorously over the real numbers and Euclidean spaces. Introductory real analysis is sometimes called advanced calculus, and studies
Real_analysis
Branch of mathematics
quantitative methods of approximation and convergence. It grew out of calculus, especially the use of derivatives and integrals to study variable quantities
Mathematical_analysis
Generalized function whose value is zero everywhere except at zero
and therefore is a Hilbert space. On the other hand, the functional that evaluates a holomorphic function in H ( D ) ∩ L 2 ( D ) {\displaystyle H(D)\cap
Dirac_delta_function
Manifold upon which it is possible to perform calculus
allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within
Differentiable_manifold
Index of articles associated with the same name
mapping theorem in functional analysis, the proof in the setting of topological groups uses the Baire category theorem. In calculus, part of the inverse
Open_mapping_theorem
Mathematical study of linear operators
(A*A)1/2 is the unique positive square root of A*A given by the usual functional calculus. So by the lemma, we have A = U ( A ∗ A ) 1 2 {\displaystyle A=U(A^{*}A)^{\frac
Operator_theory
Matrix of second derivatives
{\displaystyle f} is holomorphic, then its complex Hessian matrix is identically zero, so the complex Hessian is used to study smooth but not holomorphic functions
Hessian_matrix
Type of mathematical functions
pseudoconvexity does not characterize holomorphically convexity, and then by Lars Hörmander using methods from functional analysis and partial differential
Function of several complex variables
Function_of_several_complex_variables
Set of functions between two fixed sets
of type − × X {\displaystyle -\times X} on objects; In functional programming and lambda calculus, function types are used to express the idea of higher-order
Function_space
satisfying a very mild completeness condition. Traditional differential calculus is effective in the analysis of finite-dimensional vector spaces and for
Convenient_vector_space
Derivative defined on normed spaces
function of multiple real variables, and to define the functional derivative used widely in the calculus of variations. Generally, it extends the idea of the
Fréchet_derivative
Functions in mathematics
harmonic functions of two variables are: The real or imaginary part of any holomorphic function. In fact, all harmonic functions defined on the plane are of
Harmonic_function
Integral transform useful in probability theory, physics, and engineering
the Laplace transform gives a one-to-one correspondence between the holomorphic functions which, for some σ ∈ R {\displaystyle \sigma \in \mathbb {R}
Laplace_transform
Fundamental construction of differential calculus
are holomorphic functions, which are complex-valued functions on the complex numbers where the Fréchet derivative exists. In geometric calculus, the
Generalizations of the derivative
Generalizations_of_the_derivative
theorem of algebra Lambda calculus Invariance of domain Minkowski inequality Nash embedding theorem Open mapping theorem (functional analysis) Product topology
List_of_mathematical_proofs
American mathematician
(1955), Functionals of Finite Riemann Surfaces, Princeton University Press Nickerson, H. K.; Spencer, D. C.; Steenrod, N. E. (1959), Advanced Calculus, Princeton
Donald_C._Spencer
Canadian-American mathematician (1925–2020)
algebraic condition under which an almost complex structure arises from a holomorphic coordinate atlas.[NN57] The Newlander-Nirenberg theorem is now considered
Louis_Nirenberg
space, then it is equivalent to the usual orthogonality. Borel Borel functional calculus c c space. Calkin The Calkin algebra on a Hilbert space is the quotient
Glossary of functional analysis
Glossary_of_functional_analysis
Mathematical generalization of boundedness
vector or operator-valued distributions, and extending the holomorphic functional calculus of Gelfand (which is primarily concerted with Banach algebras
Bornology
Italian mathematician (1879–1943)
especially differential equations, functional analysis, and complex analysis; but he also studied the calculus of variations, group theory, non-Euclidean
Guido_Fubini
Superconductivity theory
Struwe, "Asymptotic limits of a Ginzberg-Landau type functional", Geometric Analysis and the Calculus of Variations for Stefan Hildebrandt (1996) International
Ginzburg–Landau_theory
Mathematical function, denoted exp(x) or e^x
\exp(w).} Among complex functions, it is the unique solution which is holomorphic at the point z = 0 {\displaystyle z=0} and takes the derivative
Exponential_function
Inverse of a finite difference
In the calculus of finite differences, the indefinite sum (or antidifference operator), denoted by ∑ x {\textstyle \sum _{x}} or Δ − 1 {\displaystyle \Delta
Indefinite_sum
Theory in theoretical physics
the calculations in topological string theory generically encode all holomorphic quantities within the full string theory whose values are protected by
Topological_string_theory
Type of continuous linear operator
In functional analysis, a branch of mathematics, a compact operator is a linear operator that behaves, in several important respects, like a finite-dimensional
Compact_operator
Mathematical approximation of a function
series of some smooth function. In complex analysis, however, every holomorphic function is analytic. A function whose Taylor series converges to the
Taylor_series
French mathematician (1789–1857)
was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field of complex analysis
Augustin-Louis_Cauchy
Study of vector bundles, principal bundles, and fibre bundles
{\displaystyle E\to \Sigma } is a holomorphic vector bundle and Φ : E → E ⊗ K {\displaystyle \Phi :E\to E\otimes K} is a holomorphic endomorphism of E {\displaystyle
Gauge_theory_(mathematics)
Branch of mathematics
manifolds, complex algebraic varieties, and complex analytic varieties, and holomorphic vector bundles and coherent sheaves over these spaces. Special examples
Geometry
Topological space that locally resembles Euclidean space
manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric on a manifold allows distances and angles
Manifold
analytic continuation An analytic continuation of a holomorphic function is a unique holomorphic extension of the function (on a connected open subset
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
Branch of mathematics
otherwise known as smooth manifolds. It uses the techniques of vector calculus, linear algebra and multilinear algebra. The field has its origins in the
Differential_geometry
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating that
Mean_value_theorem
Italian mathematician (1922–1996)
[Results concerning the solutions of linear functional equations due to the National Institute for Calculus Applications], Atti della Accademia Nazionale
Gaetano_Fichera
Mathematical functions of split-complex numbers
& Rosa in their article "Hyperbolic Calculus" (1998). The Cauchy–Riemann equations that characterize holomorphic functions on a domain in the complex
Motor_variable
Topological quantum field theory
D5-branes is a 6-dimensional variant of Chern–Simons theory known as holomorphic Chern–Simons theory. Chern–Simons theories are related to many other
Chern–Simons_theory
Point of interest for complex multi-valued functions
Shantanu (2011), "Fractional Differintegrations Insight Concepts", Functional Fractional Calculus, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 213–269
Branch_point
In functional analysis, a Hilbert space
In functional analysis, a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
Objects that generalize functions
led to investigation of the idea of hyperfunction, in which spaces of holomorphic functions are used as test functions. A refined theory has been developed
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Fundamental trigonometric functions
)^{s-1}\Gamma (1-s)\sin \left({\frac {\pi }{2}}s\right)\zeta (1-s).} As a holomorphic function, sin z is a 2D solution of Laplace's equation: Δ u ( x 1 , x
Sine_and_cosine
Number with a real and an imaginary part
locally be written as f(z)/(z − z0)n with a holomorphic function f, still share some of the features of holomorphic functions. Other functions have essential
Complex_number
Series of mathematics textbooks
Analysis on Fock Spaces, Kehe Zhu, (2012, ISBN 978-1-4419-8800-3) Functional Analysis, Calculus of Variations and Optimal Control, Francis H. Clarke, (2013
Graduate_Texts_in_Mathematics
Type of mathematical expression
chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics
Polynomial
Distance from zero to a number
A Functional Approach to Graphing and Problem Solving. Jones & Bartlett Publishers. p. 8. ISBN 978-0-7637-5177-7. Spivak, Michael (1965). Calculus on
Absolute_value
German mathematician (1826–1866)
equivalent" (i.e. there is a bijection between them that is holomorphic with a holomorphic inverse) to either C {\displaystyle \mathbb {C} } or to the
Bernhard_Riemann
exp X will also have strictly positive eigenvalues. By the holomorphic functional calculus the exponential map on the space of operators with real spectrum
Invariant_convex_cone
Typically linear operator defined in terms of differentiation of functions
commutative algebra. See also Jet (mathematics). In the development of holomorphic functions of a complex variable z = x + i y, sometimes a complex function
Differential_operator
Mathematics of convex functions and sets
convex sets, convex functions, and their applications to optimization, functional analysis, variational analysis, convex geometry, economics, and related
Convex_analysis
Functions of an angle
which are (by definition) complex-valued functions that are defined and holomorphic on the whole complex plane. Term-by-term differentiation shows that the
Trigonometric_functions
Number, approximately 3.14
definition because, as Remmert 2012 explains, differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to
Pi
American mathematician and Nobel Laureate (1928–2015)
and Moser's techniques. From the fact that minimizers to many functionals in the calculus of variations solve elliptic partial differential equations,
John_Forbes_Nash_Jr.
Mathematical theorem
Introduce eitQ and eisP, the corresponding unitary groups given by functional calculus. (For the explicit operators x and p defined above, these are multiplication
Stone–von_Neumann_theorem
Irish mathematician (1944–2024)
dimensional complex analysis and the topological structure of spaces of Holomorphic functions. He later worked on bounded symmetric domains and spectral
Seán_Dineen
American mathematician
than 350 scholarly articles and 160 books. Krantz, Steven G. (1980), "Holomorphic functions of bounded mean oscillation and mapping properties of the Szegő
Steven_G._Krantz
American mathematician (born 1931)
3, 727–785. Driver, Bruce K.; Gross, Leonard; Saloff-Coste, Laurent: Holomorphic functions and subelliptic heat kernels over Lie groups. J. Eur. Math
Leonard_Gross
Product of numbers from 1 to n
its scalar multiples are the only holomorphic functions on the positive complex half-plane that obey the functional equation and remain bounded for complex
Factorial
Field theory involving topological effects in physics
the theory is the number of pseudo holomorphic maps f : M → X in the sense of Gromov (they are ordinary holomorphic maps if X is a Kähler manifold). If
Topological quantum field theory
Topological_quantum_field_theory
Quantum field theory enjoying conformal symmetry
copies of the Virasoro algebra. In Euclidean CFT, these copies are called holomorphic and antiholomorphic. In Lorentzian CFT, they are called left-moving and
Conformal_field_theory
Four-dimensional number system
Ghiloni, R.; Moretti, V.; Perotti, A. (2013). "Continuous slice functional calculus in quaternionic Hilbert spaces". Rev. Math. Phys. 25 (4): 1350006–126
Quaternion
equations Pia Nalli (1884–1964), Italian researcher in functional analysis and tensor calculus Seema Nanda, Indian researcher in applications of mathematics
List_of_women_in_mathematics
Italian mathematician (1912–1982)
[Results regarding the solution of linear functional equations due to the National Institute for Calculus Applications], Rendiconti di Matematica e delle
Carlo_Miranda
Arithmetic operation
exponentiation is holomorphic for z ≠ 0 , {\displaystyle z\neq 0,} in the sense that its graph consists of several sheets that define each a holomorphic function
Exponentiation
Japanese mathematician
theory for the total scalar curvature functional for riemannian metrics and related topics". Topics in Calculus of Variations (PDF). Vol. 1365. Berlin
Morio_Obata
morphisms, and a well-defined subcategory of analytic geometry objects and holomorphic mappings. Armand Borel, Jean-Pierre Serre (1958) Borel and Serre's exposition
List of publications in mathematics
List_of_publications_in_mathematics
Number whose square is a given number
{2}}e^{i(3\pi /4)}=-1+i=-{\sqrt {-2i}}.} The principal square root function is holomorphic everywhere except on the set of non-positive real numbers (on strictly
Square_root
Extension of the factorial function
continuation of this integral function: it is a meromorphic function which is holomorphic except at zero and the negative integers, where it has simple poles.
Gamma_function
meromorphic function f. The meromorphic differential df = dU + idV is holomorphic everywhere except for a double pole at P with singular term d(z−1) at
Planar_Riemann_surface
Tensor in differential geometry
The canonical line bundle is the top exterior power of the bundle of holomorphic Kähler differentials: κ = ⋀ n Ω X . {\displaystyle \kappa ={\textstyle
Ricci_curvature
Every polynomial has a real or complex root
similar argument also gives a proof of the maximum modulus principle for holomorphic functions). Continuing from before the principle was invoked, if a :=
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Concept in mathematics
equation for a mapping also arises as the Euler-Lagrange equation of a functional called the Dirichlet energy. As such, the theory of harmonic maps contains
Harmonic_map
History of maths
character on X. Ideally the moduli spaces should be a critical sets of holomorphic Chern–Simons functions and the Donaldson–Thomas invariants should be
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Mathematics of smooth surfaces
S2CID 119253397. Guilfoyle, B.; Klingenberg, W. (2020). "Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces". Ann. Fac. Sci. Toulouse
Differential geometry of surfaces
Differential_geometry_of_surfaces
Mathematics, University of Minnesota, Twin Cities: Finite element exterior calculus. Shimon Attie, Visual Artist, Brooklyn, New York: Video installation. Dean
List of Guggenheim Fellowships awarded in 2008
List_of_Guggenheim_Fellowships_awarded_in_2008
HOLOMORPHIC FUNCTIONAL-CALCULUS
HOLOMORPHIC FUNCTIONAL-CALCULUS
Boy/Male
English
The fictional character Jorel father of Superman.
Boy/Male
Australian, French
Fictional Swordsman; Ambitious and Filled with Religious Aspirations; From Alexander Dumas's Three Musketeers
Male
Egyptian
, Functionary of the Interior.
Male
Celtic
, great justiciary, or functionary.
Boy/Male
American, Australian, British, Danish, English, Finnish, French, German, Scandinavian
Farmer; The Fictional Character Jorel Father of Superman; Earth Worker
Biblical
Look for pages within Wikipedia that link to this title
If a page was recently created here it may not be visible yet because of a delay in updating the database; wait a few minutes or try the function.
Look for pages within Wikipedia that link to this title
Male
Egyptian
, a great functionary.
Boy/Male
French
Fictional swordsman: (ambitious and filled with religious aspirations) from Alexander Dumas's...
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, an Egyptian functionary.
Boy/Male
English
The fictional character Jorel father of Superman.
Boy/Male
English
The fictional character Jorel father of Superman.
Male
Egyptian
, an Egyptian functionary.
Boy/Male
American, British, English
Mighty Spearman; The Fictional Character Jorel Father of Superman
Boy/Male
American, British, English
Mighty Spearman; One who Saves; The Fictional Character Jorel Father of Superman
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, a high Egyptian functionary.
Boy/Male
English
Modern. The fictional character Jorel father of Superman.
Boy/Male
American, Australian, British, English, French
Mighty Spearman; The Fictional Character Jorel Father of Superman
HOLOMORPHIC FUNCTIONAL-CALCULUS
HOLOMORPHIC FUNCTIONAL-CALCULUS
Girl/Female
German English
The earth.
Surname or Lastname
English
English : habitational name from some minor place, probably the one in West Yorkshire, called Ogden, from Old English Äc ‘oak’ + denu ‘valley’.
Girl/Female
Indian, Punjabi, Sikh
My; Mine
Boy/Male
Hindu, Indian
Useful to All
Boy/Male
Gujarati, Hindu, Indian, Kannada, Sanskrit
To Expand; Progress
Girl/Female
English American
Abbreviation of Jaqueline which is the feminine of Jacques.
Boy/Male
Indian, Punjabi, Sikh
The Blessed One
Boy/Male
Indian
Concealed, Veiled
Male
English
Variant spelling of English Eric, ARIC means "ever-ruler."
Girl/Female
American, Australian, British, Chinese, Christian, English, French, Greek, Indian, Irish, Jamaican, Norse, Romanian, Scottish
Violet; Island; Flower Name; Blessed; Amethyst; Dove; Scottish Island; Purple Gem; Beach Strand
HOLOMORPHIC FUNCTIONAL-CALCULUS
HOLOMORPHIC FUNCTIONAL-CALCULUS
HOLOMORPHIC FUNCTIONAL-CALCULUS
HOLOMORPHIC FUNCTIONAL-CALCULUS
HOLOMORPHIC FUNCTIONAL-CALCULUS
v. i.
Alt. of Functionate
a.
Pertaining to the function of an organ or part, or to the functions in general.
a.
Of or pertaining to allomorphism.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
a.
Pertaining to, or connected with, a function or duty; official.
a.
Of, pertaining to, or characterized by, trimorphism; -- contrasted with monomorphic, dimorphic, and polymorphic.
a.
Of or pertaining to zoomorphism.
a.
Of or pertaining to fractions or a fraction; constituting a fraction; as, fractional numbers.
v. i.
To execute or perform a function; to transact one's regular or appointed business.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
a.
Relatively small; inconsiderable; insignificant; as, a fractional part of the population.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
a.
Alt. of Monomorphous
a.
Relating to friction; moved by friction; produced by friction; as, frictional electricity.
v. t.
To supply with an organ or organs having a special function or functions.
a.
Polymorphous.
a.
Fractional.
adv.
In a functional manner; as regards normal or appropriate activity.
a.
Having, or occurring in, several distinct forms; -- opposed to monomorphic.
a.
Alt. of Homomorphous