On a left-α-ψ-hyperholomorphic Bergman space

Given a structural set , some papers [M. Shapiro, V. Vasilevski, (Complex Var Theory Appl. 1995;27:17-46 and 1995;27:67-96)] study the quaternionic ψ-Fueter operator calculus, where the Fueter-type operator is The aim of this paper is to present the function theory and the Bergman theory induced by...

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Vydáno v:Complex variables and elliptic equations Ročník 68; číslo 2; s. 222 - 236
Hlavní autor: González-Cervantes, J. Oscar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Colchester Taylor & Francis 01.02.2023
Taylor & Francis Ltd
Témata:
conformally covariant property
Operators (mathematics)
quaternionic reproducing kernel
Quaternionic weighted Bergman spaces
α-hyperholomorphy function theory
ISSN:1747-6933, 1747-6941
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Shrnutí:Given a structural set , some papers [M. Shapiro, V. Vasilevski, (Complex Var Theory Appl. 1995;27:17-46 and 1995;27:67-96)] study the quaternionic ψ-Fueter operator calculus, where the Fueter-type operator is The aim of this paper is to present the function theory and the Bergman theory induced by the ψ-Fueter-type operator: where a is a quaternionic constant and f is a continuously differentiable function. Particularly, this work shows the Stokes and Borel-Pompieu formulas associated to and presents several results of the Bergman theory such as the existence of the Bergman kernel, Bergman projection and their conformal covariant properties.
Bibliografie:ObjectType-Article-1
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ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2021.1986033