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Generalized Almansi Expansions in Superspace

Generalized Almansi Expansions in Superspace In this paper, we first study an expansion for the operators $$\begin{aligned} (\partial _{x}-\lambda )^{k}, \end{aligned}$$ ( ∂ x - λ ) k , where $$\partial _{x}$$ ∂ x is the Dirac operator in superspace and $$\lambda $$ λ is a complex number. Then we investigate expansions for polynomial Dirac operators in superspace. These expansions are regarded as generalized Almansi expansions in superspace. As an application of the expansions, the modified Riquier problem in superspace is considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Generalized Almansi Expansions in Superspace

Computational Methods and Function Theory , Volume 16 (3) – Jan 19, 2016

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References (21)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-015-0153-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we first study an expansion for the operators $$\begin{aligned} (\partial _{x}-\lambda )^{k}, \end{aligned}$$ ( ∂ x - λ ) k , where $$\partial _{x}$$ ∂ x is the Dirac operator in superspace and $$\lambda $$ λ is a complex number. Then we investigate expansions for polynomial Dirac operators in superspace. These expansions are regarded as generalized Almansi expansions in superspace. As an application of the expansions, the modified Riquier problem in superspace is considered.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 19, 2016

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