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Function that "converges" to periodicity
In mathematics, an almost periodic function is, loosely speaking, a function of a real variable that is periodic to within any desired level of accuracy
Almost_periodic_function
Function with a repeating pattern
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which are used to describe waves
Periodic_function
Subset of a topological space whose closure is compact
its closure is the whole non-compact space. The definition of an almost periodic function F at a conceptual level has to do with the translates of F being
Relatively_compact_subspace
Mathematical notion of recurrence with unpredictable period
strictly defined mathematical concepts such as an almost periodic function or a quasiperiodic function. Climate oscillations that appear to follow a regular
Quasiperiodicity
almost periodic functions on G to the theory of continuous functions on H. The concept is named after Harald Bohr who pioneered the study of almost periodic
Bohr_compactification
Class of functions behaving "like" periodic functions
In mathematics, a quasiperiodic function is a function that has a certain similarity to a periodic function. A function f {\displaystyle f} is quasiperiodic
Quasiperiodic_function
Mean-periodic functions are a separate generalization of periodic functions from the almost periodic functions. For instance, exponential functions are
Mean-periodic_function
Term in set theory
almost all real numbers in (0, 1) are members of the complement of the Cantor set. Look up almost in Wiktionary, the free dictionary. Almost periodic
Almost
Tabular arrangement of the chemical elements
The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows ("periods") and columns
Periodic_table
Type of motion that is approximately periodic
of quasi-periodic functions, by Ernest Esclangon following the work of Piers Bohl, in fact led to a definition of almost-periodic function, the terminology
Quasiperiodic_motion
Planetary motions in archaic models of the Solar System
z_{2}=z_{0}+z_{1}=a_{0}e^{ik_{0}t}+a_{1}e^{ik_{1}t}\,.} This is an almost periodic function, and is a periodic function just when the ratio of the constants kj is rational
Deferent_and_epicycle
Duality for locally compact abelian groups
mathematical notion of duality. John von Neumann (1934) studied almost periodic functions on groups and extended harmonic analysis beyond countable settings
Pontryagin_duality
Russian mathematician (1891–1970)
Rockefeller Fellowship, where he worked on almost periodic functions under Harald Bohr. A type of function space in that field now bears his name. After
Abram_Besicovitch
Linear mathematical operator which translates a function
on functions of a real variable plays an important role in harmonic analysis, for example, it appears in the definitions of almost periodic functions, positive-definite
Shift_operator
Danish mathematician and footballer (1887–1951)
Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr
Harald_Bohr
Ordered chemical structure with no repeating pattern
(mathematician brother of Niels Bohr). The concept of an almost periodic function (also called a quasiperiodic function) was studied by Bohr, including work of Bohl
Quasicrystal
Hungarian and American mathematician and physicist (1903–1957)
beginning with a paper on almost periodic functions on groups, where von Neumann extended Bohr's theory of almost periodic functions to arbitrary groups. He
John_von_Neumann
Episodes of muscular weakness due to low blood potassium levels
develop symptoms of periodic paralysis due to hyperthyroidism (overactive thyroid). This entity is distinguished with thyroid function tests, and the diagnosis
Hypokalemic periodic paralysis
Hypokalemic_periodic_paralysis
(7 June 1914 – 4 April 2004) was a mathematician who worked on almost periodic functions, Sturm–Liouville operators and inverse scattering. Levitan was
Boris_Levitan
Function with unusual fractal properties
is represented by a periodic continued fraction, so the value of the question-mark function on x {\displaystyle x} is a periodic binary fraction and thus
Minkowski's question-mark function
Minkowski's_question-mark_function
Point which a function/system returns to after some time or iterations
iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations
Periodic_point
Embedding a topological space into a compact space as a dense subset
compactification of a topological group arises from the consideration of almost periodic functions. The projective line over a ring for a topological ring may compactify
Compactification (mathematics)
Compactification_(mathematics)
Measure-preserving dynamical system Ergodic theory Mixing (mathematics) Almost periodic function Symbolic dynamics Time scale calculus Arithmetic dynamics Sequential
List of dynamical systems and differential equations topics
List_of_dynamical_systems_and_differential_equations_topics
music – Resonance – Sonoluminescence – Speed of light – Sunspot Almost periodic function – Amplitude modulation – Amplitude – Beat – Chaos theory – Cyclic
List_of_cycles
Quantum Mechanics 1961. Volume II: Operators, Ergodic Theory and Almost Periodic Functions in a Group 1961. Volume III: Rings of Operators 1962. Volume IV:
List of scientific publications by John von Neumann
List_of_scientific_publications_by_John_von_Neumann
the boundedness over the entire real axis of the integral of an almost-periodic function. The ultimate form of this inequality was given by Jean Favard;
Bohr–Favard_inequality
Decomposition of periodic functions
of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a
Fourier_series
Polynomial function of degree two
representation of conic sections Quadric Periodic points of complex quadratic mappings List of mathematical functions Weisstein, Eric Wolfgang. "Quadratic
Quadratic_function
Austrian mathematician (1899–1982)
MR 1151393 Bochner almost periodic functions Bochner–Kodaira–Nakano identity Bochner Laplacian Bochner measurable function "[the st-and.ac.uk "Biography"
Salomon_Bochner
Wavefunctions Uncertainty principle Quantum Fourier transform Periodic function Almost periodic function ATS theorem Modulus of continuity Banach algebra Compact
List of Fourier analysis topics
List_of_Fourier_analysis_topics
Everywhere except a set of measure zero
Everywhere of Rademacher's Series and of the Bochnerfejér Sums of a Function almost Periodic in the Sense of Stepanoff". Proceedings of the London Mathematical
Almost_everywhere
Oscillatory error in Fourier series
continuously differentiable periodic function around a jump discontinuity. The N {\textstyle N} th partial Fourier series of the function (formed by summing the
Gibbs_phenomenon
American award for mathematical analysis
1938 John von Neumann for Almost periodic functions. I. Trans. Amer. Math. Soc. 36 (1934), 445-294 Almost periodic functions. II. Trans. Amer. Math. Soc
Bôcher_Memorial_Prize
Multi-element, directional antenna useable over a wide band of frequencies
A log-periodic antenna (LP), also known as a log-periodic array or log-periodic aerial, is a multi-element, directional antenna designed to operate over
Log-periodic_antenna
German mathematician
of almost periodic sequences of numbers (Zur Theorie der fastperiodischen Zahlfolgen). It was a topic from the theory of almost periodic functions suggested
Ingeborg_Seynsche
Soviet mathematician and theoretical physicist (1909–1992)
as direct methods of the calculus of variations, the theory of almost periodic functions, methods of approximate solution of differential equations, and
Nikolay_Bogolyubov
Special function occurring in problems possessing elliptic symmetry
including Mathieu functions of fractional order as well as non-periodic solutions. Closely related are the modified Mathieu functions, also known as radial
Mathieu_function
Danish mathematician (1919–1991)
from 1954 to 1974. Følner published a comprehensive survey of almost periodic functions with Harald Bohr, and continued with further studies on this topic
Erling_Følner
Left-invariant (or right-invariant) measure on locally compact topological group
mean value of compactly supported functions is zero. However something like this does work for almost periodic functions on the group which do have a mean
Haar_measure
Italian electrical engineer and mathematician (1912–2004)
electrical engineer and mathematician. He is known for his work on almost periodic functions, on Laplace transforms in one and several dimensions, and on the
Luigi_Amerio
Method of visualizing the relationship between elements
A period on the periodic table is a row of chemical elements. All elements in a row have the same number of electron shells. Each next element in a period
Period_(periodic_table)
Extension of the factorial function
give a unique solution, since it allows for multiplication by any periodic function g ( x ) {\displaystyle g(x)} with g ( x ) = g ( x + 1 ) {\displaystyle
Gamma_function
Integral expressing the amount of overlap of one function as it is shifted over another
be defined for functions on Euclidean space and other groups (as algebraic structures).[citation needed] For example, periodic functions, such as the discrete-time
Convolution
Blumenthal (1876–1944), mathematician Harald Bohr (1887–1951), almost periodic functions Vladimir Boltyansky (1925–2019), mathematician and educator Carl
List_of_Jewish_mathematicians
Simple polynomial map exhibiting chaotic behavior
the number of periodic points is countably infinite, and so almost all orbits starting from initial values are not periodic but non-periodic. One of the
Logistic_map
Equation in Fourier analysis
the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely
Poisson_summation_formula
of degree n in some real algebraic number field K of degree n. Almost periodic function Yves Meyer, Algebraic numbers and harmonic analysis, North-Holland
Harmonious_set
Pontryagin duality Kronecker's theorem on diophantine approximation Almost periodic function Bohr compactification Wiener's tauberian theorem Representation
List of harmonic analysis topics
List_of_harmonic_analysis_topics
Central African mathematician and politician
ISBN 0-7872-9404-7. N'Guérékata, Gaston Mandata (2001). Almost automorphic and almost periodic functions in abstract spaces. Springer Science & Business Media
Gaston_N'Guérékata
Ryll-Nardzewski, C. (1962). "Generalized random ergodic theorems and weakly almost periodic functions". Bull. Acad. Polon. Sci. Sér. Sci. Math. Astron. Phys. 10: 271–275
Ryll-Nardzewski fixed-point theorem
Ryll-Nardzewski_fixed-point_theorem
Development of the table of chemical elements
The periodic table is an arrangement of the chemical elements, structured by their atomic number, electron configuration and recurring chemical properties
History_of_the_periodic_table
Characteristic of an optical system
x)} , as a function of the spatial frequency, ν {\displaystyle \nu } , while its complex argument indicates a phase shift in the periodic pattern. The
Optical_transfer_function
S-shaped curve
be modeled as a periodic function (of period T {\displaystyle T} ) or (in case of continuous infusion therapy) as a constant function, and one has that
Logistic_function
Mathematical rule
I {\displaystyle f:I\to I} is a continuous function. The number x {\displaystyle x} is called a periodic point of period m {\displaystyle m} if f ( m
Sharkovskii's_theorem
Role of coherent states
integral in Bohr's sense, like it is in use in the theory of almost periodic functions. Actually the construction of Gazeau–Klauder CS can be extended
Coherent states in mathematical physics
Coherent_states_in_mathematical_physics
Korean Interactive table in Vietnamese English-Chinese periodic table of elements The Chinese Periodic Table: A Rosetta Stone for Understanding the Language
Chemical elements in East Asian languages
Chemical_elements_in_East_Asian_languages
Latvian mathematician (1865–1921)
quasi-periodic functions. The notion of quasi-periodic functions was generalised still further by Harald Bohr when he introduced almost periodic functions.
Piers_Bohl
Periodic table of the elements with eight or more periods
Extended periodic table Element 119 (Uue, marked here) in period 8 (row 8) marks the start of theorisations. An extended periodic table theorizes about
Extended_periodic_table
Generalized version of classical Green's function
Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations
Multiscale_Green's_function
Mathematical transform that expresses a function of time as a function of frequency
endpoints identified). The latter is routinely employed to handle periodic functions. The fast Fourier transform (FFT) is an algorithm for computing the
Fourier_transform
Function that is discontinuous at rationals and continuous at irrationals
Thomae's function is a real-valued function of a real variable that can be defined as: f ( x ) = { 1 q if x = p q ( x is rational), with p ∈ Z and
Thomae's_function
Theoretical framework in harmonic analysis
series of a periodic Lp function (p > 1) and nj is a sequence satisfying nj+1/nj > q for some fixed q > 1, then the sequence Snj converges almost everywhere
Littlewood–Paley_theory
of Technology Integral equations, orthogonal functions, and their relation to almost periodic functions Harry Shultz Vandiver University of Texas, Austin
List of Guggenheim Fellowships awarded in 1927
List_of_Guggenheim_Fellowships_awarded_in_1927
Model in Quantum Physics
periodic function with a period a. According to Bloch's theorem, the wavefunction solution of the Schrödinger equation when the potential is periodic
Particle in a one-dimensional lattice
Particle_in_a_one-dimensional_lattice
Mathematical theory on dynamical systems
contracting, then there is no periodic orbit. Formally, the theorem asserts that if there exists a C 1 {\displaystyle C^{1}} function φ ( x , y ) {\displaystyle
Bendixson–Dulac_theorem
Bronze medal awarded by the Royal Society (London)
outstanding work on almost-periodic functions, the theory of measure and integration and many other topics of theory of functions." 1955 — Edward Charles
Sylvester_Medal
Weyl–Groenewold product Wigner–Weyl transform Weyl algebra Weyl almost periodic functions Weyl anomaly Weyl basis of the gamma matrices Weyl chamber Weyl
List of things named after Hermann Weyl
List_of_things_named_after_Hermann_Weyl
Periodic recurrence of the quantum wave function
In quantum mechanics, quantum revival is a periodic recurrence of the quantum wave function during its time-evolution. This can be either many times in
Quantum_revival
Generalized function whose value is zero everywhere except at zero
series associated with a periodic function converges to the function. The n-th partial sum of the Fourier series of a function f of period 2π is defined
Dirac_delta_function
alumnus of the department; his research in harmonic analysis and almost periodic functions in the 1930s laid the foundation for a huge drive in analysis
UCPH Department of Mathematical Sciences
UCPH_Department_of_Mathematical_Sciences
Mathematical problem in classical harmonic analysis
question of whether the Fourier series of a given periodic function converges to the given function is studied in classical harmonic analysis, a branch
Convergence_of_Fourier_series
Describes the range of energies of an electron within the solid
gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been
Electronic_band_structure
Concept in mathematical analysis
mathematical analysis, the Dirichlet kernel, is the collection of periodic functions defined as D n ( x ) = ∑ k = − n n e i k x = ( 1 + 2 ∑ k = 1 n cos
Dirichlet_kernel
Irregular alternation different types of dynamics
intermittency). Experimentally, intermittency appears as long periods of almost periodic behavior interrupted by chaotic behavior. As control variables change
Intermittency
Sum of all proper divisors of a natural number
a prime number, a perfect number, or a periodic sequence of sociable numbers. Sum of positive divisors function, the sum of the (xth powers of the) positive
Aliquot_sum
Integral transform and linear operator
{\displaystyle H(f)(x)=-i{\bigl (}F_{+}(x)+F_{-}(x){\bigr )}.} For a periodic function f the circular Hilbert transform is defined: f ~ ( x ) ≜ 1 2 π p
Hilbert_transform
Nearest integers from a number
Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less
Floor_and_ceiling_functions
Chemical element with atomic number 1 (H)
Physics C. 45 (3) 030001. doi:10.1088/1674-1137/abddae. "Element: Hydrogen". Periodic table. Retrieved 21 January 2026. NAAP Labs (2009). "Energy Levels". University
Hydrogen
Visualization of sudden behavior changes caused by continuous parameter changes
approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system.
Bifurcation_diagram
Romanian-American theologian
Corduneanu, Constantin; Gheorghiu, N.; Barbu, Viorel (1968). Almost Periodic Functions. Interscience Tracts in pure and applied Mathematics. Vol. 22
Constantin_Corduneanu
Semi-analytic method of computational electromagnetism
Floquet's theorem that the solutions of periodic differential equations can be expanded with Floquet functions (or sometimes referred as a Bloch wave,
Rigorous coupled-wave analysis
Rigorous_coupled-wave_analysis
Mathematical function, inverse of an exponential function
{2-{\sqrt {3}}}}} is not. Almost all real numbers are transcendental. The logarithm is an example of a transcendental function. The Gelfond–Schneider theorem
Logarithm
Doubling map on the unit interval
initial condition is irrational (as almost all points in the unit interval are), then the dynamics are non-periodic—this follows directly from the definition
Dyadic_transformation
Energy release on formation of anions
Einitial)detach = ΔE(detach) = −ΔE(attach). Although Eea varies greatly across the periodic table, some patterns emerge. Generally, nonmetals have more positive Eea
Electron_affinity
the qualitative theory of ordinary differential equations, and almost periodic functions (extending the work of Harald Bohr). In the qualitative theory
Vyacheslav_Stepanov
Set of functions used to represent the electronic wave function
second period of the periodic system (Li – Ne) would have a basis set of five functions (two s functions and three p functions). A minimal basis set
Basis_set_(chemistry)
2010 book by Sam Kean
discusses how the periodic table would not function if it were not for the layout. He states that an element's position describes its function and strength
The_Disappearing_Spoon
Techniques and methods in signal processing
object, rather than separately. A simple example is that the 4-fold periodicity of the Fourier transform – and the fact that two-fold Fourier transform
Time–frequency_analysis
1966 result in mathematical analysis
extended by Hunt, can be formally stated as follows: Let f be an Lp periodic function for some p ∈ (1, ∞], with Fourier coefficients f ^ ( n ) {\displaystyle
Carleson's_theorem
Statistical model
can be defined through the covariance function are the process' stationarity, isotropy, smoothness and periodicity. Stationarity refers to the process'
Gaussian_process
Square root of the mean square
RMS over all time of a periodic function is equal to the RMS of one period of the function. The RMS value of a continuous function or signal can be approximated
Root_mean_square
Function describing an electron in an atom
wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of all elements in the periodic table
Atomic_orbital
Interference pattern
by the sinusoidal envelope "beat" function cos(Bx), whose periodic variation is half the difference of the periodic variations k1 and k2 (and evidently
Moiré_pattern
Open problem on 3x+1 and x/2 functions
almost all (in the sense of logarithmic density) Collatz orbits descend below any given function of the starting point, provided that this function diverges
Collatz_conjecture
Summability method in physics
on the walls of the box and which are periodic in τ with period β. In this situation from the partition function he computes energy, entropy and pressure
Zeta_function_regularization
geometry Norbert Wiener Massachusetts Institute of Technology Bohr's almost periodic functions Medicine and Health Julian Herman Lewis University of Chicago
List of Guggenheim Fellowships awarded in 1926
List_of_Guggenheim_Fellowships_awarded_in_1926
Type of zeta function
function is a zeta function associated with a scheme of finite type over integers. The arithmetic zeta function generalizes the Riemann zeta function
Arithmetic_zeta_function
Number whose square is a given number
square root function f ( x ) = x {\displaystyle f(x)={\sqrt {x}}} (usually just referred to as the "square root function") is a function that maps the
Square_root
Covering by shapes without overlaps or gaps
can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings
Tessellation
Function whose domain is the positive integers
Arithmetical Functions. An introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties,
Arithmetic_function
ALMOST PERIODIC-FUNCTION
ALMOST PERIODIC-FUNCTION
Boy/Male
British, English
From the Old Cottage
Boy/Male
Norse Scandinavian American Gaelic Scottish
Lawyer.
Male
Egyptian
, child of the moon.
Girl/Female
German
Of Noble Spirit
Girl/Female
Biblical
Hidden.
Boy/Male
American, Australian, Chinese, Christian, Jamaican, Norse, Scandinavian, Scottish
Lawyer; Law Man; Man of Law
Boy/Male
Christian & English(British/American/Australian)
Lawyer
Girl/Female
Arabic, Muslim
Diamond
Boy/Male
Czech
Determined; stubborn.
Girl/Female
Indian, Indonesian, Italian
Gift of God; Periodic
Boy/Male
Scandinavian
Surname.
Surname or Lastname
English
English : ostensibly a topographic name containing Middle English cott, cote ‘cottage’ (see Coates). In fact, however, it is generally if not always an alteration of Alcock, in part at least for euphemistic reasons.Louisa May Alcott (1832–88), author of Little Women (1869), was the daughter of Amos Bronson Alcott (1799–1888), who had changed the family name from Alcox. The family trace their descent from an Alcocke family who emigrated from England to MA with John Winthrop in 1629.
Boy/Male
Hawaiian
Strong (Hawaiian interpretation of the name Amos).
Girl/Female
Indian
A diamond
Boy/Male
Czech, Czechoslovakian, German
Determined; Stubborn; Sincere
Girl/Female
Muslim
Diamond. Adamant.
Boy/Male
American, British, English
From the Old Cottage
Male
English
Scottish surname transferred to English forename use, from the medieval Swedish personal name Lagman, LAMONT means "lawman."
Girl/Female
Swedish
Pearl.
Boy/Male
German
Power of an Eagle
ALMOST PERIODIC-FUNCTION
ALMOST PERIODIC-FUNCTION
Female
Welsh
Welsh form of Greek Elisabet, BETHAN means "God is my oath."Â
Boy/Male
Indian, Sanskrit
To Worship
Boy/Male
English
Lives in the valley.
Boy/Male
Hindu
Guarded, Secure, Saved
Male
English
German name derived from the word braun, BRUNO means "brown."Â In use by the English.
Boy/Male
Gujarati, Indian, Kannada
Fire
Boy/Male
Australian, Danish, French, German, Swedish
Bear
Boy/Male
Indian, Sanskrit
Heart as Big as Ocean
Girl/Female
Hindu
Surname or Lastname
English and German
English and German : variant spelling of Johns or Jones. This spelling is also found in Finland.
ALMOST PERIODIC-FUNCTION
ALMOST PERIODIC-FUNCTION
ALMOST PERIODIC-FUNCTION
ALMOST PERIODIC-FUNCTION
ALMOST PERIODIC-FUNCTION
a.
Of or pertaining to a period or periods, or to division by periods.
adv.
Almost.
a.
Related to, or formed from, pyridin or its homologues; as, the pyridic bases.
a.
Situated at the farthest point or extremity; farthest out; most distant; extreme; as, the utmost limits of the land; the utmost extent of human knowledge.
n.
The fruit of the almond tree.
a.
Performed in a period, or regular revolution; proceeding in a series of successive circuits; as, the periodical motion of the planets round the sun.
a.
Of or pertaining to a period; constituting a complete sentence.
a.
Most distant; farthest.
n.
The most that can be; the farthest limit; the greatest power, degree, or effort; as, he has done his utmost; try your utmost.
a.
Being in the greatest or highest degree, quantity, number, or the like; greatest; as, the utmost assiduity; the utmost harmony; the utmost misery or happiness.
n.
The tree that bears the fruit; almond tree.
adv.
Nearly; well nigh; all but; for the greatest part.
n.
Alms.
a.
Happening, by revolution, at a stated time; returning regularly, after a certain period of time; acting, happening, or appearing, at fixed intervals; recurring; as, periodical epidemics.
n.
One of the great divisions of geological time; as, the Tertiary period; the Glacial period. See the Chart of Geology.
a.
Alt. of Periodical
n.
Anything shaped like an almond.
a.
Surrounding, or pertaining to the region surrounding, the internal ear; as, the periotic capsule.
n.
A periotic bone.
v. i.
To come to a period; to conclude. [Obs.] "You may period upon this, that," etc.