The Monogenic Cauchy–Kovalevskaya Extension in Two Vector Variables

The Monogenic Cauchy–Kovalevskaya Extension in Two Vector Variables The Cauchy–Kovalevskaya extension for polynomials in several variables is a crucial result in Clifford analysis which describes theoretically how to construct simplicial monogenics in m dimensions starting from certain polynomial spaces in $$m-1$$ m - 1 dimensions, hereby using the so-called branching rules. In [13] it was shown that the Cauchy–Kovalevskaya extension map is an isomorphism of the kernel of the wedge operator onto the space of spherical monogenics in two variables. The aim of this paper is to show that this extension maps simplicial polynomials of the kernel of the wedge operator just onto the simplicial monogenics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

The Monogenic Cauchy–Kovalevskaya Extension in Two Vector Variables

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
ISSN
0188-7009
eISSN
1661-4909
D.O.I.
10.1007/s00006-018-0846-y
Publisher site
See Article on Publisher Site

Abstract

The Cauchy–Kovalevskaya extension for polynomials in several variables is a crucial result in Clifford analysis which describes theoretically how to construct simplicial monogenics in m dimensions starting from certain polynomial spaces in $$m-1$$ m - 1 dimensions, hereby using the so-called branching rules. In [13] it was shown that the Cauchy–Kovalevskaya extension map is an isomorphism of the kernel of the wedge operator onto the space of spherical monogenics in two variables. The aim of this paper is to show that this extension maps simplicial polynomials of the kernel of the wedge operator just onto the simplicial monogenics.

Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Feb 24, 2018

References

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