Results 1 to 10 of about 347 (160)

On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H₄(a,b;c,d;z₁,z₂) Ratios

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are constructed.
Tamara Antonova, Roman Dmytryshyn, Ilona-Anna Lutsiv, Serhii Sharyn   +3 more
doaj   +1 more source

The boundary values of holomorphic functions of several complex variables

Duke Mathematical Journal, 1977
Edgar Lee Stout
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On the Analytic Continuation of Lauricella–Saran Hypergeometric Function F_K(a₁,a₂,b₁,b₂;a₁,b₂,c₃;z)

Mathematics, 2023
The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions FK with some parameter values to the corresponding branched continued fractions in their domain of convergence.
Tamara Antonova, Roman Dmytryshyn, Vitaliy Goran   +2 more
doaj   +1 more source

Boundedness of the L-index in a direction of the sum and product of slice holomorphic functions in the unit ball

Математичні Студії, 2022
Let $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice $\{z^0+t\mathbf{
V.P. Baksa, A. I. Bandura, T.M. Salo
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Slice holomorphic functions in the unit ball: boundedness of $L$-index in a direction and related properties

Математичні Студії, 2022
Let $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice $\{z^0+t\mathbf{
A. I. Bandura, T. M. Salo, O. B. Skaskiv
doaj   +1 more source

$L^2$ extension theorem for jets with variable denominators

Comptes Rendus. Mathématique, 2021
By studying the variable denominators introduced by X. Zhou–L. Zhu, we generalize the results of D. Popovici for the $L^2$ extension theorem for jets. As a direct corollary, we also give a generalization of T. Ohsawa–K. Takegoshi’s extension theorem to a
Rao, Sheng, Zhang, Runze
doaj   +1 more source

Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains

Boundary Value Problems, 2010
Monogenic extension theorem of complex Clifford algebras-valued functions over a bounded domain with fractal boundary is obtained. The paper is dealing with the class of Hölder continuous functions.
Paul Bosch, Ricardo Abreu-Blaya, Juan Bory-Reyes   +2 more
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Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc

Discrete Analysis, 2023
Bi-parameter potential theory and Carleson measures for the Dirichlet space on the bidisc, Discrete Analysis 2023:22, 58 pp. Carleson measures arise naturally when considering harmonic or holomorphic extensions from the boundary of a domain to the ...
Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt, Giulia Sarfatti   +3 more
doaj   +1 more source

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, Maria Martsinkiv, Oleh Skaskiv   +2 more
doaj   +1 more source

Boundary values and estimates for holomorphic functions of several complex variables

Duke Mathematical Journal, 1980
Steven G. Krantz
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