Pólya’s theorem for entire functions of two complex variables

1963 ◽  
pp. 311-314
Author(s):  
A. A. Kozmanova
Keyword(s):  
Entire Functions ◽  
Complex Variables ◽  
Polya's Theorem ◽  
Pólya’S Theorem

scholarly journals On Pólya’s Theorem in several complex variables

2015 ◽  
Vol 107 ◽  
pp. 149-157
Author(s):  
Ozan Günyüz ◽  
Vyacheslav Zakharyuta
Keyword(s):  
Complex Variables ◽  
Several Complex Variables ◽  
Polya's Theorem ◽  
Pólya’S Theorem

A note on Pólya’s theorem

1984 ◽  
Vol 35 (1) ◽  
pp. 104-111
Author(s):  
Dinis Pestana
Keyword(s):  
Polya's Theorem ◽  
Pólya’S Theorem

scholarly journals Mean-periodic functions

1980 ◽  
Vol 3 (2) ◽  
pp. 199-235 ◽  
Author(s):  
Carlos A. Berenstein ◽  
B. A. Taylor
Keyword(s):  
Partial Differential Equations ◽  
Periodic Function ◽  
Entire Functions ◽  
Convolution Equation ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Exponential Polynomial ◽  
Periodic Functions ◽  
Open Questions ◽  
Constant Coefficients

We show that any mean-periodic functionfcan be represented in terms of exponential-polynomial solutions of the same convolution equationfsatisfies, i.e.,u∗f=0(μ∈E′(ℝn)). This extends ton-variables the work ofL. Schwartz on mean-periodicity and also extendsL. Ehrenpreis' work on partial differential equations with constant coefficients to arbitrary convolutors. We also answer a number of open questions about mean-periodic functions of one variable. The basic ingredient is our work on interpolation by entire functions in one and several complex variables.

scholarly journals ON CERTAIN SUB-SPACE OF X

2008 ◽  
Vol 5 (4) ◽  
pp. 660-668
Author(s):  
Baghdad Science Journal
Keyword(s):  
Entire Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Topological Properties

The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex variables which is studied by Kamthan.

On a generalization of Pólya’s theorem

2007 ◽  
Vol 81 (1-2) ◽  
pp. 247-259 ◽  
Author(s):  
I. P. Rochev
Keyword(s):  
Polya's Theorem ◽  
Pólya’S Theorem

On Pólya's Theorem

1967 ◽  
Vol 19 ◽  
pp. 792-799 ◽  
Author(s):  
J. Sheehan
Keyword(s):  
Finite Groups ◽  
Scalar Product ◽  
Combinatorial Analysis ◽  
Simple Extension ◽  
Group Characters ◽  
Polya's Theorem ◽  
Representations Of Finite Groups ◽  
Pólya’S Theorem ◽  
Special Case ◽  
Superposition Theorem

In 1927 J. H. Redfield (9) stressed the intimate interrelationship between the theory of finite groups and combinatorial analysis. With this in mind we consider Pólya's theorem (7) and the Redfield-Read superposition theorem (8, 9) in the context of the theory of permutation representations of finite groups. We show in particular how the Redfield-Read superposition theorem can be deduced as a special case from a simple extension of Pólya's theorem. We give also a generalization of the superposition theorem expressed as the multiple scalar product of certain group characters. In a later paper we shall give some applications of this generalization.

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