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Bounded index, entire solutions of ordinary differential equations and summability methods [PDF]
International Journal of Mathematics and Mathematical Sciences, 1981 A brief survey of recent results on functions of bounded index and bounded index summability methods is given. Theorems on entire solutions of ordinary differential equations with polynomial coefficients are included.
G. H. Fricke, Ranjan Roy, S. M. Shah
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Математичні Студії, 2023 There is introduced a concept of index for the Fueter regular function of the quaternionic variables. There are considered three approaches (Fueter, Sudbery and Mariconda) constructing the Fueter regular function from a holomorphic function of complex ...
V. P. Baksa, A. I. Bandura
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Note on composition of entire functions and bounded $L$-index in direction
Математичні Студії, 2021 We study the following question: ``Let $f\colon \mathbb{C}\to \mathbb{C}$ be an entire function of bounded $l$-index, $\Phi\colon \mathbb{C}^n\to \mathbb{C}$ an be entire function, $n\geq2,$ $l\colon \mathbb{C}\to \mathbb{R}_+$ be a continuous function ...
A. I. Bandura, O. B. Skaskiv, T. M. Salo
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Demonstratio Mathematica, 2019 In the paper we investigate slice holomorphic functions F : ℂn → ℂ having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 + tb : t ∈ℂ} for an arbitrary z0 ∈ℂn and for the fixed direction b ∈ℂn \ {0}, and (∃m0 ∈ ℤ+) (∀m ∈
Bandura Andriy +2 more
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Entire functions of bounded index in frame
Математичні Студії, 2020 We introduce a concept of entire functions having bounded index in a variable direction, i.e. in a frame. An entire function $F\colon\ \mathbb{C}^n\to \mathbb{C}$ is called a function of bounded frame index in a frame $\mathbf{b}(z)$, if~there exists ...
A.I. Bandura
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Researches in MathematicsFor functions analytic in the unit polydisc with bounded $L$-index in a direction there are presented three various results. The product theorem specifies that the product of analytic functions of bounded $L$-index in direction belongs to the same class.
A.I. Bandura +4 more
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Vector-Valued Entire Functions of Several Variables: Some Local Properties
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 Bivariate Functions of Exponential Type II
Математичні Студії, 2023 Let $f(z_{1},z_{2})$ be a bivariate entire function and $C$ be a positive constant. If $f(z_{1},z_{2})$ satisfies the following inequality for non-negative integer $M$, for all non-negative integers $k,$ $l$ such that $k+l\in\{0, 1, 2, \ldots, M\}$, for ...
A. Bandura, F. Nuray
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Slice Holomorphic Functions in the Unit Ball Having a Bounded L-Index in Direction
Axioms, 2020 Let b∈Cn\{0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e., we study functions that are analytic in the intersection of every slice {z0+tb:t∈C} with the unit ball Bn={z∈C:|z|:=|z|12 ...
Andriy Bandura +2 more
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Note on boundedness of the $L$-index in the direction of the composition of slice entire functions
Математичні Студії, 2022 We study a composition of two functions belonging to a class of slice holomorphic functions in the whole $n$-dimensional complex space. The slice holomorphy in the space means that for some fixed direction $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\
V. P. Baksa +3 more
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