IJPAM: Volume 79, No. 2 (2012)

ON SOME TRANSMUTATIONS FOR LINEAR PARTIAL
DIFFERENTIAL EQUATIONS OF FIRST AND
SECOND ORDER IN CLIFFORD ANALYSIS

Peter Berglez
Department of Mathematics
Graz University of Technology
Steyrergasse 30, 8010, Graz, AUSTRIA


Abstract. Using the Clifford algebra we consider a generalization of the Cauchy-Riemann system. These equations are related to some important equations such as the Maxwell equations, the Dirac equation and the Moisil-Theodorescu system.

With the help of first-order and higher-order partial differential operators, transmutations of holomorphic functions, their relatives and of solutions of certain related differential equations to the equations considered here are given. For the first time explicit representations for a class of generalized Clifford holomorphic functions obeying a generalized Bers-Vekua equation are derived and relations between the solutions of the characterizing differential equations with different parameters are presented. Similar representations and relations are given for the solutions of a differential equation of second order also.

Received: August 3, 2011

AMS Subject Classification: 30G20, 30G35, 35C05

Key Words and Phrases: generalized Cauchy-Riemann system, transmutations, differential operators, Clifford analysis

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 2