On the Definition of Higher Gamma Functions: On the definition of higher gamma functions

Authors: Pérez-Marco, Ricardo

Contributors: Pérez-Marco, Ricardo

Source: Constructive Approximation. 61:413-443

Subject Terms: 30D15 Gamma function, Representations of entire functions of one complex variable by series and integrals, Mathematics - Complex Variables, multiple gamma functions, Special classes of entire functions of one complex variable and growth estimates, History of special functions, Mellin Gamma functions, 2010 Mathematics Subject Classification. Primary: 33B15. Secondary: 30D10, 01 natural sciences, gamma function, 33B15, 30D10, 30D15, Barnes Gamma function, Mathematics - Classical Analysis and ODEs, Jackson \(q\)-gamma function, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mellin gamma functions, Jackson q-Gamma function, Barnes gamma function, 0101 mathematics, Complex Variables (math.CV), Gamma, beta and polygamma functions, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2101.01291
https://zbmath.org/8018007
https://doi.org/10.1007/s00365-023-09674-w
https://hal.science/hal-03096445v1/document
https://doi.org/10.1007/s00365-023-09674-w
https://hal.science/hal-03096445v1

Extension of Turán-type inequalities for polar derivatives of polynomials into integral mean version

Authors: Chanam, Barchand

Source: Publications de l'Institut Mathematique. 116:75-85

Subject Terms: polar derivative, polynomials, Polynomials and rational functions of one complex variable, Turán type inequalities, Special classes of entire functions of one complex variable and growth estimates, Inequalities in the complex plane, \(L^r\)-norm inequalities

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Entire functions sharing two small functions with their difference operators

Authors: Majumder, Sujoy, Sarkar, Nabadwip

Source: ANNALI DELL'UNIVERSITA' DI FERRARA. 70:249-271

Subject Terms: uniqueness, Special classes of entire functions of one complex variable and growth estimates, Strong solutions to PDEs, entire functions of finite order, sharing values

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Two problems on random analytic functions in Fock spaces

Authors: Xiang Fang, Pham Trong Tien

Source: Canadian Journal of Mathematics. 75:1176-1198

Subject Terms: Random power series in one complex variable, mixed-norm space, Bergman spaces and Fock spaces, Special classes of entire functions of one complex variable and growth estimates, random analytic functions, Fock spaces, 0101 mathematics, 01 natural sciences

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A growth aspect of entire functions of infinite order

Authors: Singh, J. P.

Source: Publicationes Mathematicae Debrecen. 23:249-253

Subject Terms: Entire functions of one complex variable (general theory), Representations of entire functions of one complex variable by series and integrals, Dirichlet series, exponential series and other series in one complex variable, Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/3460633

Logarithmic mean function of entire functions defined by Dirichlet series

Authors: Gupta, J. S., Singh, Manjit

Source: Publicationes Mathematicae Debrecen. 20:13-19

Subject Terms: Representations of entire functions of one complex variable by series and integrals, Dirichlet series, exponential series and other series in one complex variable, Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/3450563

Growth of geometric means of an entire function

Authors: Singh, J. P.

Source: Publicationes Mathematicae Debrecen. 21:161-169

Subject Terms: Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/3480936

On entire functions of slow growth

Authors: Bundschuh, P.

Source: Publicationes Mathematicae Debrecen. 27:17-24

Subject Terms: interpolation series, Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, entire functions of slow growth, 01 natural sciences

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Access URL: https://zbmath.org/3719467

Interpolation of entire functions on regular sparse sets and q-Taylor series: Interpolation of entire functions on regular sparse sets and \(q\)-Taylor series

Authors: Michael Welter

Source: Journal de théorie des nombres de Bordeaux. 17:397-404

Subject Terms: Basic hypergeometric functions in one variable, \({}_r\phi_s\), \(q\)-calculus and related topics, Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, Moment problems and interpolation problems in the complex plane, 01 natural sciences, Interpolation in approximation theory

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Access URL: http://www.numdam.org/item/10.5802/jtnb.497.pdf
https://zbmath.org/2205452
https://doi.org/10.5802/jtnb.497
https://www.math.uni-bonn.de/people/welter/JTNB_2005__17_1_397_0.pdf
https://eudml.org/doc/249438
http://almira.math.u-bordeaux.fr/jtnb/2005-1/pages397-404.pdf

Radial distribution of zeros of entire functions and sections of their power series

Authors: Hamdan, May F., Abi-Khuzam, Faruk F.

Subject Terms: Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Special classes of entire functions of one complex variable and growth estimates, sections of Taylor series, zero distribution

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Access URL: https://zbmath.org/2208338

Permissible growth rates for Birkhoff type universal harmonic functions

Authors: Armitage, David

Source: Journal of Approximation Theory. 136:230-243

Subject Terms: Translation, Mathematics(all), Numerical Analysis, Applied Mathematics, name=Analysis, Harmonic, Density, name=Applied Mathematics, Special classes of entire functions of one complex variable and growth estimates, Growth, name=Numerical Analysis, 01 natural sciences, Harmonic, subharmonic, superharmonic functions in higher dimensions, name=General Mathematics, harmonic function, universal function, growth rate, 0101 mathematics, Universal, Analysis

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Access URL: https://dblp.uni-trier.de/db/journals/jat/jat136.html#Armitage05
https://pure.qub.ac.uk/portal/en/publications/permissible-growth-rates-for-birkhoff-type-universal-harmonic-functions(eebc45e3-9644-4cf6-9aa3-49eab3b33d0c).html
https://dialnet.unirioja.es/servlet/articulo?codigo=1276620
https://pure.qub.ac.uk/en/publications/permissible-growth-rates-for-birkhoff-type-universal-harmonic-fun
https://core.ac.uk/display/82279755
https://www.sciencedirect.com/science/article/pii/S0021904505001383

A UNIQUENESS THEOREM IN THE INVERSE SPECTRAL THEORY OF A CERTAIN HIGHER-ORDER ORDINARY DIFFERENTIAL EQUATION USING PALEY–WIENER METHODS: A uniqueness theorem in the inverse spectral theory of a certain higher-order ordinary differential equation using Paley-Wiener methods

Authors: Erik Andersson

Source: Journal of the London Mathematical Society. 72:169-184

Subject Terms: Representations of entire functions of one complex variable by series and integrals, Inverse problems involving ordinary differential equations, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), General theory of ordinary differential operators, inverse problem, spectral measure, Special classes of entire functions of one complex variable and growth estimates, Paley-Wiener theorem, 0101 mathematics, 01 natural sciences, Weyl theory and its generalizations for ordinary differential equations

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Access URL: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024610704005770
https://documat.unirioja.es/servlet/articulo?codigo=2207499
https://dialnet.unirioja.es/servlet/articulo?codigo=2522803
https://academic.oup.com/jlms/article-abstract/72/1/169/864939
https://portal.research.lu.se/sv/publications/a-uniqueness-theorem-in-the-inverse-spectral-theory-of-a-certain-
https://www.cambridge.org/core/journals/journal-of-the-london-mathematical-society/article/uniqueness-theorem-in-the-inverse-spectral-theory-of-a-certain-higherorder-ordinary-differential-equation-using-paleywiener-methods/E509C78C63CE12D98B443B26A0C63786

Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves: Asymptotic behavior of the sum of the Dirichlet series of prescribed growth on curves

Authors: A. M. Gaisin, I. D. Latypov

Source: Mathematical Notes. 78:33-46

Subject Terms: entire function, Dirichlet series, exponential series and other series in one complex variable, Special classes of entire functions of one complex variable and growth estimates, 0102 computer and information sciences, Dirichlet series, 0101 mathematics, order in the Ritt sense, 01 natural sciences

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Access URL: https://zbmath.org/2239719
https://doi.org/10.1007/s11006-005-0096-x
https://rd.springer.com/article/10.1007%2Fs11006-005-0096-x
https://link.springer.com/article/10.1007/s11006-005-0096-x

A new class of integer-valued entire functions

Authors: Michael Welter

Source: Journal für die reine und angewandte Mathematik (Crelles Journal). 2005:175-192

Subject Terms: Transcendence (general theory), Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, 01 natural sciences

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Access URL: https://www.degruyter.com/view/j/crll.2005.2005.issue-583/crll.2005.2005.583.175/crll.2005.2005.583.175.xml

On an Asymptotic Equality Between the Minimum and the Maximum of δ-Subharmonic Functions of Zero Genus: On an asymptotic equality between the minimum and the maximum of \(\delta\)-subharmonic functions of zero genus

Authors: Igor Chyzhykov, Oleh Skaskiv

Source: Computational Methods and Function Theory. 4:447-460

Subject Terms: Riesz charge, \(\delta\)-subharmonic functions of zero genus, Riesz measures, Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, Harmonic, subharmonic, superharmonic functions in two dimensions, 01 natural sciences

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Access URL: https://zbmath.org/2186790
https://doi.org/10.1007/bf03321080
https://link.springer.com/article/10.1007/BF03321080

A Carleman-Nevanlinna Theorem and Summation of the Riemann Zeta-Function Logarithm: A Carleman-Nevanlinna theorem and summation of the Riemann zeta-function logarithm

Authors: Andriy A. Kondratyuk

Source: Computational Methods and Function Theory. 4:391-403

Subject Terms: Carleman-Nevanlinna theorem, summation, \(\zeta (s)\) and \(L(s, \chi)\), meromorphic function, Special classes of entire functions of one complex variable and growth estimates, 0101 mathematics, 01 natural sciences, Euler product, Riemann zeta-function, Riemann hypothesis

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Access URL: https://zbmath.org/2186786
https://doi.org/10.1007/bf03321076
https://link.springer.com/article/10.1007%2FBF03321076

Spectral synthesis for the intersection of invariant subspaces of holomorphic functions: Spectral synthesis for the intersection of invariant subspaces of holomorphic functions.

Authors: Bulat N. Khabibullin

Source: Sbornik: Mathematics. 196:423-445

Subject Terms: spectral synthesis, Invariant subspaces of linear operators, differentiation invariant subspaces, holomorphic functions, Spaces of bounded analytic functions of one complex variable, Special classes of entire functions of one complex variable and growth estimates, Topological linear spaces of continuous, differentiable or analytic functions, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2210567
https://doi.org/10.1070/sm2005v196n03abeh000886
http://ui.adsabs.harvard.edu/abs/2005SbMat.196..423K/abstract

Interpolation of functions from generalized Paley–Wiener spaces: Interpolation of functions from generalized Paley--Wiener spaces

Authors: W. R. Madych, Yu. Lyubarskii

Source: Journal of Approximation Theory. 133:251-268

Subject Terms: Mathematics(all), Numerical Analysis, Applied Mathematics, Special classes of entire functions of one complex variable and growth estimates, 02 engineering and technology, 01 natural sciences, generalized Paley-Wiener space, interpolation, Paley—Wiener spaces, Banach spaces of continuous, differentiable or analytic functions, 0202 electrical engineering, electronic engineering, information engineering, Complete interpolating sequences, ∂¯ problem, Divided differences, 0101 mathematics, Analysis

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Access URL: https://zbmath.org/2160167
https://doi.org/10.1016/j.jat.2004.12.014
https://dblp.uni-trier.de/db/journals/jat/jat133.html#LyubarskiiM05
https://dialnet.unirioja.es/servlet/articulo?codigo=1361828
https://www.sciencedirect.com/science/article/pii/S0021904505000031
https://core.ac.uk/display/82180251

Almost strict total positivity and a class of Hurwitz polynomials

Authors: Dimitrov, D. K., Pena, J. M.

Contributors: Universidade Estadual Paulista (UNESP)

Source: Repositório Institucional da UNESP
Universidade Estadual Paulista (UNESP)
instacron:UNESP

Subject Terms: Mathematics(all), Numerical Analysis, Entire function in the Laguerre–Pólya class, Totally positive matrix, Applied Mathematics, Inequalities involving derivatives and differential and integral operators, Special classes of entire functions of one complex variable and growth estimates, strictly totally positive matrix, 01 natural sciences, Hurwitz polynomial, Positive matrices and their generalizations, cones of matrices, Strictly totally positive matrix, totally positive matrix, shadows' lemma, entire function in the Laguerre-Polya class, Hurwitz stable polynomial, 0101 mathematics, Laguerre-Pólya class, Shadows' lemma, Analysis

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Access URL: https://zbmath.org/2165383
https://doi.org/10.1016/j.jat.2004.10.010

BINOMIAL SUMS AND FUNCTIONS OF EXPONENTIAL TYPE: Binomial sums and functions of exponential type

Authors: Javad Mashreghi, Thomas Ransford

Source: Bulletin of the London Mathematical Society. 37:15-24

Subject Terms: Inequalities, stochastic orderings, Phragmén Lindelöf theorem, Special classes of entire functions of one complex variable and growth estimates, General theory of topological algebras, 0101 mathematics, Factorials, binomial coefficients, combinatorial functions, 01 natural sciences, sequence of complex numbers, Poisson random variable

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Access URL: https://zbmath.org/2162699
https://doi.org/10.1112/s0024609304003625
https://academic.oup.com/blms/article/37/1/15/280984
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0024609304003625
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024609304003625
https://www.cambridge.org/core/journals/bulletin-of-the-london-mathematical-society/article/binomial-sums-and-functions-of-exponential-type/DC194D1D38D61ACABF0BB44D97CD2188