Results 1 to 10 of about 28,571 (151)

Removable sets for holomorphic functions of several complex variables [PDF]

Publicacions Matemàtiques, 1989
We show that every closed subset of CN that has finite (2N-2) dimensional measure is a removable set for holomorphic functions, and we obtain a related result on the ...
Stout, Edgar Lee
core   +11 more sources

ON IDENTICAL VANISHING OF HOLOMORPHIC FUNCTIONS IN SEVERAL COMPLEX VARIABLES. [PDF]

Proc Natl Acad Sci U S A, 1959
Bochner S.
europepmc   +5 more sources

Representation of Some Ratios of Horn’s Hypergeometric Functions H₇ by Continued Fractions

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7 ...
Tamara Antonova, Roman Dmytryshyn, Pavlo Kril, Serhii Sharyn   +3 more
doaj   +1 more source

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

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
doaj   +1 more source

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

Variations on Hartogs and Henkin-Tumanov Theorems [PDF]

, 2007
There are equivalent characterizations for holomorphic functions defined on open sets of $\mathbb C^n$; first of all, they can be represented locally as sums of convergent power series.
Mascolo, Raffaella
core   +5 more sources

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
doaj   +2 more sources