Dirichlet series, sequences of Dirichlet polynomials, and functional equations connected with them

DOI10.1007/BF01223130zbMath0398.30015MaRDI QIDQ1254423

A. F. Leont'ev

Publication date: 1975

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

BibliographyDirichlet SeriesConvolution EquationDirichlet Series with Complex ExponentsEquations of Infinite OrderExpansion of Functions in Dirichlet SeriesFunctions Representable By Dirichlet Series with Real ExponentsInvariant Subspaces of FunctionsRepresentation By Multiple Dirichlet SeriesRepresentation of Analytic Functions of Several VariablesSequences of Dirichlet Polynomials

Mathematics Subject Classification ID

Spaces of bounded analytic functions of one complex variable (30H05) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Dirichlet series, exponential series and other series in one complex variable (30B50) Polynomials and rational functions of one complex variable (30C10) Representations of entire functions of one complex variable by series and integrals (30D10) Special classes of entire functions of one complex variable and growth estimates (30D15)

Cites Work

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• Factorization of a convolution-type operator
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• On the ordinary proximate linear orders of integral functions defined by Dirichlet series
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• On entire Dirichlet series of zero order
• Über die Konvergenz Dirichletscher Polynome
• On the maximum term of an integral function defined by Dirichlet series
• On the lower order of an entire function defined by Dirichlet series
• Asymptotische Approximation stetiger Funktionen durch ganze Dirichlet- Reihen
• On the geometric means of an entire function represented by Dirichlet series
• Zulässige Abänderungen von Exponentialsystemen im \(L^ p(-A,A)\)
• Multiple series of Dirichlet polynomials
• On the representation of functions by Dirichlet double series
• Régularité et suprarégularité pour une famille de germes dirichlétiens (par rapport à un support de référence)
• Some problems of the theory of growth of functions defined by series of functions \(\{f(\lambda_ n z)\}\)
• On the mean values of an entire function represented by Dirichlet series
• Proximate order of entire Dirichlet functions
• Influence des propriétés arithmétiques des exposants d'une série de Dirichlet sur son prolongement analytique. (Influence of the arithmetic properties of the exponents of a Dirichlet series upon its analytic extension.)
• On the lower order of an entire Dirichlet series
• The problem of representations by multiple Dirichlet series
• The completeness of spaces of Dirichlet series with sufficiently sparse complex exponents
• On the multiplication of Dirichlet series
• Transformees de Fourier de fonctions entières et séries de Dirichlet. Un principe de dualité
• Théorie générale des fonctions moyenne-périodiques
• Un problème de composition des singularités des séries de Dirichlet générales
• Note on Dirichlet series. V: On the integral functions defined by Dirichlet series. (I.)
• Sets of convergence of ordinary Dirichlet series
• Über analytische Lösungen linearer Differential- Differenzengleichungen
• A NOTE ON ENTIRE FUNCTIONS (DEFINED BY DIRICHLET'S SERIES) OF PERFECTLY REGULAR GROWTH
• Sur les points singuliers des séries de Dirichlet d'une classe de Cramer
• Region of Convergence of Dirichlet Series with Complex Exponents
• ON AN EXPANSION IN EXPONENTIAL SERIES
• ON THE LOWER ORDER OF ENTIRE FUNCTIONS DEFINED BY DIRICHLET SERIES
• On Absolutely Convergent Dirichlet Series
• On Julia-lines of Dirichlet series
• Mandelbrojt's Inequality and Dirichlet Series with Complex Exponents
• On the Domain of Absolute Convergence of Dirichlet Series in Several Variables
• On Entire Functions Defined by a Dirichlet Series
• On Absolutely Convergent Exponential Sums
• On Entire Functions Defined by a Dirichlet Series: Correction
• On the Maximum Modulus and the Maximum Term of an Entire Dirichlet Series
• Sur l'approximation pondérée par des polynomes et par des sommes d'exponentielles imaginaires
• On the Order of Integral Functions Defined by Dirichlet Series
• On the Mean Values of Integral Functions and Their Derivatives Defined by Dirichlet Series
• Some Gap Theorems for Dirichlet Series
• ON THE RITT ORDER OF ENTIRE DIRICHLET SERIES
• Zeros of Exponential Sums
• On entire functions represented by Dirichlet series
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• The Ritt order of the derivative of an entire function
• On the mean square modulus of an entire Dirichlet series
• Coefficient Estimates for Lacunary Power Series and Dirichlet Series. I
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• On the Order of Integral Functions Defined by Dirichlet Series
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• Infinite Order Differential Equations
• Coefficient Estimates for Dirichlet Series
• Un exemple dans la théorie du prolongement analytique d'une série de Dirichlet
• On entire functions of slow growth represented by Dirichlet series
• ON THE MEAN CONVERGENCE OF A CERTAIN CLASS OF EXPONENTIAL SERIES
• Derivative of generalized quadratic mean function of entire functions defined by Dirichlet series
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