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Vector-Valued Entire Functions of Several Variables: Some Local Properties [PDF]
Axioms, 2022 The present paper is devoted to the properties of entire vector-valued functions of bounded L-index in join variables, where L:Cn→R+n is a positive continuous function.
Andriy Ivanovych Bandura +2 more
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Entire Functions of Several Variables: Analogs of Wiman’s Theorem
AxiomsThis article considers a class of entire functions of several complex variables that are bounded in the Cartesian product of some half-planes. Each such hyperplane is defined on the condition that the real part of the corresponding variable is less than ...
Oleh Skaskiv +3 more
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Fractal and Fractional, 2023 The composition H(z)=f(Φ(z)) is studied, where f is an entire function of a single complex variable and Φ is an entire function of n complex variables with a vanished gradient.
Andriy Bandura +2 more
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ON THE EXCEPTIONAL SET OF TRANSCENDENTAL ENTIRE FUNCTIONS IN SEVERAL VARIABLES
Bulletin of the Australian Mathematical Society, 2023 AbstractWe prove that any subset of $\overline {\mathbb {Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountably many transcendental entire functions over $\mathbb {C}^m$ with rational coefficients.
DIEGO ALVES +3 more
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Demonstratio Mathematica, 2023 In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in Cn{{\mathbb{C}}}^{n}. Our results are the generalizations
Haldar Goutam, Banerjee Abhijit
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Countably Generated Algebras of Analytic Functions on Banach Spaces
Axioms, 2023 In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably generated algebras often appear as algebras of symmetric analytic functions on Banach spaces with respect
Zoriana Novosad +2 more
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Approximation characteristics of the isotropic Nikol'skii-Besov functional classes
Karpatsʹkì Matematičnì Publìkacìï, 2021 In the paper, we investigates the isotropic Nikol'skii-Besov classes $B^r_{p,\theta}(\mathbb{R}^d)$ of non-periodic functions of several variables, which for $d = 1$ are identical to the classes of functions with a dominant mixed smoothness $S^{r}_{p ...
S.Ya. Yanchenko, O.Ya. Radchenko
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Advances in Difference Equations, 2021 This paper is concerned with description of the existence and the forms of entire solutions of several second-order partial differential-difference equations with more general forms of Fermat type.
Hong Yan Xu +3 more
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Zeros of entire functions in several complex variables [PDF]
Transactions of the American Mathematical Society, 1972 A geometric condition on the zero set of an entire function f in CN (N > 1) is presented which is both necessary and sufficient for f to have the same zeros as some polynomial in C 1. 1.
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Levy's phenomenon for entire functions of several variables
Уфимский математический журнал, 2013 For entire functions $f(z)=\sum_{n=0}^{+\infty}a_nz^n, z\in {\Bbb C},$ P. L${\rm \acute{e}}$vy (1929) established that in the classical Wiman's inequality $M_f(r)\leq _f(r)\times $ $\times(\ln _f(r))^{1/2+\varepsilon},\ \varepsilon>0,$ which holds outside a set of finite logarithmic measure, the constant 1/2 can be replaced almost surely in some ...
Kuryliak, Andriy +2 more
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