On the solutions of a class of iterated generalized Bers–Vekua equations in Clifford analysis

✍ Scribed by P. Berglez

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 95 KB
• Volume: 33
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1207

✦ Synopsis

Abstract

We consider functions with values in the Clifford algebra Cl~p,q~ which are solutions of a certain class of the iterated generalized Bers–Vekua equation D^m^w=0 with Dw=__∂__w+__c__w̄ where \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}$\partial={\sum\nolimits_{j=0}^{n}}e_j,\partial/{\partial x_j}$\end{document} is the generalized Cauchy–Riemann operator and x=x~0~+x~1~e~1~+…x~n~e~n~. We prove that any such function w has an Almansi‐type decomposition of the form w=v~0~+x~0~v~1~+···+x____v~__m−__1~ where the functions v~j~, j=0,1,…, __m−__1, are solutions of the generalized Bers–Vekua equation Dv=0. Copyright © 2009 John Wiley & Sons, Ltd.