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On the solutions of a class of iterated generalized Bers–Vekua equations in Clifford analysis
Author(s) -
Berglez P.
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1207
Subject(s) - mathematics , clifford analysis , iterated function , operator (biology) , class (philosophy) , cauchy–riemann equations , clifford algebra , pure mathematics , function (biology) , algebra over a field , type (biology) , mathematical analysis , mathematical physics , dirac operator , chemistry , ecology , biochemistry , repressor , artificial intelligence , evolutionary biology , biology , computer science , transcription factor , gene
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 m− 1 0v 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.