Integral kernels for k-hypermonogenic functions

Vesa Vuojamo*, Sirkka Liisa Eriksson

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

We consider the modified Cauchy–Riemann operator Mk =∑ni=0 ei∂xi+ k/xnQ in the universal Clifford algebra Cl0,n with the basis e1, . . . , en. The null-solutions of this operator are called k-hypermonogenic functions. We calculate the k-hyperbolic harmonic fundamental solutions, i.e. solutions to (Formula presented.), and use these solutions to find k-hypermonogenic kernels for a Cauchy-type integral formula in the upper half-space.

Original languageEnglish
Pages (from-to)1254-1265
Number of pages12
JournalCOMPLEX VARIABLES AND ELLIPTIC EQUATIONS
Volume62
Issue number9
DOIs
Publication statusPublished - 2 Sep 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Cauchy integral formula
  • Clifford algebra
  • hyperbolic Laplace–Beltrami
  • k-hyperbolic harmonic
  • k-hypermonogenic

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