A Remark on Holomorphic Functions Rational in Some Variables

Considering the holomorphic functions in a polycylindrical domain which are rational in some of the variables for the arbitrary fixed values of other variables, we prove that the functions are representable as a ratio of polynomials in these variables whose coefficients are holomorphic in the remain...

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Bibliographic Details
Published in:Siberian mathematical journal Vol. 65; no. 5; pp. 1112 - 1115
Main Authors: Ivanova, O. A., Melikhov, S. N.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.09.2024
Springer Nature B.V
Subjects:
Analytic functions
Complex variables
Conflicts of interest
Hankel matrices
Mathematics
Mathematics and Statistics
Polynomials
Rationality
Variables
Hankel matrix
rational function
holomorphic function
517.553
ISSN:0037-4466, 1573-9260
Online Access:Get full text
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Summary:Considering the holomorphic functions in a polycylindrical domain which are rational in some of the variables for the arbitrary fixed values of other variables, we prove that the functions are representable as a ratio of polynomials in these variables whose coefficients are holomorphic in the remaining variables. We use the Kronecker method for establishing some criterion for the rationality of a holomorphic function of one complex variable in a neighborhood of zero by using the properties of Hankel matrices.
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ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446624050112