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Analytic function in mathematics
In analysis, a lacunary function or series is an analytic function that cannot be analytically continued anywhere outside the radius of convergence within
Lacunary_function
Extension of the domain of an analytic function (mathematics)
{L}}_{c}(z^{c^{m}}),\forall |z|<1.} For any positive natural numbers c, the lacunary series function diverges at z = 1 {\displaystyle z=1} . We consider the question
Analytic_continuation
Topics referred to by the same term
band Lacunary function, an analytic function in mathematics Lacunarity, a mathematical measure of the extent that a pattern contains gaps Lacunary polynomial
Lacuna
Number not in the image of a given function
In complex analysis, a subfield of mathematics, a lacunary value or gap of a complex-valued function defined on a subset of the complex plane is a complex
Lacunary_value
Function that is holomorphic on the whole complex plane
called a lacunary value of the function. The possibility of a lacunary value is illustrated by the exponential function, which never takes on the value
Entire_function
larger open set—not even to a single point on the boundary of D. Lacunary function Fabry gap theorem Krantz, Steven G. (1999). Handbook of complex variables
Ostrowski–Hadamard gap theorem
Ostrowski–Hadamard_gap_theorem
Concept in complex analysis
holomorphy. A particular example is the open unit disk. Define the lacunary function ∑ n = 0 ∞ z 2 n {\displaystyle \textstyle \sum _{n=0}^{\infty }z^{2^{n}}}
Domain_of_holomorphy
Statistical model
violate condition (*). An example found by Marcus and Shepp is a random lacunary Fourier series X t = ∑ n = 1 ∞ c n ( ξ n cos λ n t + η n sin λ n t
Gaussian_process
Mathematical function
… , X n ) = P lacunary ( X 1 , … , X n ) + X 1 ⋯ X n ⋅ Q ( X 1 , … , X n ) . {\displaystyle P(X_{1},\ldots ,X_{n})=P_{\text{lacunary}}(X_{1},\ldots
Elementary symmetric polynomial
Elementary_symmetric_polynomial
Topics referred to by the same term
geometry The Ostrowski–Hadamard gap theorem on lacunary functions The Fabry gap theorem on lacunary functions The gap theorem of Fourier analysis, a statement
Gap_theorem_(disambiguation)
Fundamental theorem in probability theory and statistics
the original on 2017-10-31. Gaposhkin, V. F. (1966). "Lacunary series and independent functions". Russian Mathematical Surveys. 21 (6): 1–82. Bibcode:1966RuMaS
Central_limit_theorem
Mathematical theorem
unit circle is not a natural boundary. Gap theorem (disambiguation) Lacunary function Ostrowski–Hadamard gap theorem Montgomery, Hugh L. (1994). Ten lectures
Fabry_gap_theorem
Theorem about the range of an analytic function
single point, this point is called a lacunary value of the function. Great Picard's Theorem: If an analytic function f {\textstyle f} has an essential singularity
Picard_theorem
In mathematics, a sparse polynomial (also lacunary polynomial or fewnomial) is a polynomial that has far fewer terms than its degree and number of variables
Sparse_polynomial
Point where a mathematical object behaves irregularly
such a set include the lacunary series and the prime zeta function. Branch points are generally the result of a multi-valued function, such as z {\displaystyle
Singularity_(mathematics)
Series representing modular forms
ISSN 0264-9381. S2CID 250864942. Mertens, Michael H.; Rolen, Larry (2015). "Lacunary recurrences for Eisenstein series". Research in Number Theory. 1 9. arXiv:1504
Eisenstein_series
Romanian-American mathematician (1935–2025)
showed that every lacunary sequence of integers is in fact a "bad universal sequence" in L 1 {\displaystyle L_{1}} . Thus lacunary sequences are ‘canonical’
Alexandra_Bellow
American mathematician
Figà-Talamanca, Alessandro; Rider, Daniel (1966). "A theorem of Littlewood and lacunary series for compact groups". Pacific Journal of Mathematics. 16 (3): 505–514
Daniel_Rider
Topics referred to by the same term
the analytic continuation of lacunary power series Hermite–Hadamard inequality, bounding the integral of convex functions. Hadamard transform, an example
Hadamard_(disambiguation)
Sumerian myth
ultimately locates him, resulting in a mitigation of Dumuzi's fate. The lacunary text allows for several interpretations, contingent on how it is read.
Descent of Inanna into the Underworld
Descent_of_Inanna_into_the_Underworld
American mathematician
Reinhold-Larsson, Karin; Wierdl, Máté (1996). "The strong sweeping out property for lacunary sequences, Riemann sums, convolution powers and related matters". Ergodic
Roger_Jones_(mathematician)
Polish-French mathematician (1899–1983)
harmonic analysis, with an emphasis on Dirichlet series, lacunary series, and entire functions. Rather than a Bourbakist, he is perhaps more accurately
Szolem_Mandelbrojt
Unsolved problem in mathematics
02.002. S2CID 26415692. —— (May 2018). "The lonely runner problem for lacunary sequences". Discrete Mathematics. 341 (5): 1301–1306. doi:10.1016/j.disc
Lonely_runner_conjecture
Canadian–American mathematician
1090/S0002-9939-1950-0036346-7. Hirschman, I. I.; Jenkins, J. A. (1950). "On lacunary Dirichlet series". Proceedings of the American Mathematical Society. 1
James_Allister_Jenkins
Icelandic mathematician (1927–2023)
1090/S0002-9947-1957-0095428-5. hdl:1721.1/26691. MR 0095428. Helgason, Sigurdur (1958). "Lacunary Fourier series on noncommutative groups". Proceedings of the American Mathematical
Sigurður Helgason (mathematician)
Sigurður_Helgason_(mathematician)
American mathematician
doi:10.1090/S0002-9939-1950-0032705-7. ——; Jenkins, J. A. (1950). "On lacunary Dirichlet series". Proceedings of the American Mathematical Society. 1
Isidore_Isaac_Hirschman_Jr.
LACUNARY FUNCTION
LACUNARY FUNCTION
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, a great functionary.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English (Cornwall)
English (Cornwall) : metonymic occupational name for someone who worked in wash house, Middle English lavendrie.English (Cornwall) : from the Old French personal name Landri, from a Germanic name composed of the elements land ‘land’ + rīc ‘power’.
Biblical
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Boy/Male
American, Basque, British, English, Greek, Hindu, Indian
From the Grassy Plain; Laundry-man; Lion Man; Property Owner or Laundry-man
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, an Egyptian functionary.
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
, Functionary of the Interior.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Boy/Male
British, English
Property Owner; Laundry-man
Male
Egyptian
, a high Egyptian functionary.
LACUNARY FUNCTION
LACUNARY FUNCTION
Boy/Male
Hindu, Indian, Marathi
Success; Win; Victory
Girl/Female
Indian
Like Sun Rays
Girl/Female
Hindu
Wet
Boy/Male
Tamil
Upagupta | உபாகà¯à®ªà¯à®¤à®¾Â
Name of a buddhist monk
Boy/Male
Hindu, Indian
Delight
Boy/Male
Gaelic
Son of the one who served Saint Michael.
Surname or Lastname
English
English : probably a variant of Budge.
Boy/Male
Indian
Old Arabic name
Male
English
Pet form of English Gerard, GED means "spear strong."
Boy/Male
Tamil
Manwendra | மாநவேநà¯à®¤à¯à®°Â Â
King among men
LACUNARY FUNCTION
LACUNARY FUNCTION
LACUNARY FUNCTION
LACUNARY FUNCTION
LACUNARY FUNCTION
pl.
of Laundry
pl.
of Lacuna
pl.
of Lacuna
pl.
of Lacunar
n.
The ceiling or under surface of any part, especially when it consists of compartments, sunk or hollowed without spaces or bands between the panels.
a.
Alt. of Lacunar
n.
A place or room where laundering is done.
pl.
of Lacunar
a.
Milky; full of white juice like milk.
n.
An outbuilding for washing, esp. one for washing clothes; a laundry.
a.
Laminar.
n.
A lacunar.
n.
a dairyhouse.
a.
Pertaining to, or having, lacunae; as, a lacunar circulation.
n.
The herb lunary or honesty. See Honesty.
v. t.
in laundry work, to dry without smoothing or ironing.
n.
A laundering; a washing.
a.
Using a noose, as a gladiator.
n.
A lacuna.
n.
One of the sunken panels in such a ceiling.