Boundary value problems of conjugate and generalized k-holomorphic functions in ℂ2

In this paper, conjugate k -holomorphic functions and generalized k -holomorphic functions are defined in the two-dimensional complex space, and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders. By the characteristics of the correspo...

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Bibliographic Details
Published in:Acta mathematica scientia Vol. 44; no. 5; pp. 1837 - 1852
Main Authors: Cui, Yanyan, Wang, Chaojun, Xie, Yonghong, Qiao, Yuying
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.09.2024
Springer Nature B.V
Edition:English Ed.
Subjects:
Analysis
Boundary value problems
Inverse problems
Mathematical functions
Mathematics
Mathematics and Statistics
Partial differential equations
32A30
30C45
holomorphic functions
partial difference equations
several complex variables
polyanalytic functions
partial difference equa-tions
κ-holomorphic functions
ISSN:0252-9602, 1572-9087
Online Access:Get full text
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Summary:In this paper, conjugate k -holomorphic functions and generalized k -holomorphic functions are defined in the two-dimensional complex space, and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders. By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k -holomorphic kernels, the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion, and the integral expressions of the solutions are obtained.
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ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-024-0511-6