An Integral Representation Formula for Multi Meta- φ -Monogenic Functions of Second Class

Abstract:

Consider the following operator (Formula presented.)where φ(j) is a Clifford-valued function and λ(j) is a Clifford-constant defined by (Formula presented.) with m= m1+ ⋯ + mn, a1= m0= 0 and aj= m1+ ⋯ + mj-1 for j= 2 , … , n; and φi(j) can be real-valued functions defined in Rm1+1×Rm2+1×⋯×Rmn+1. λi(j) are real numbers for i= 0 , 1 , … , mj and j= 1 , … , n. A function u is multi meta- φ-monogenic of second class, in several variables x(j), for j= 1 , … , n, if Dφ(j),λ(j)u=0.In this paper we give a Cauchy-type integral formula for multi meta-φ-monogenic of second class operator in one way by iteration and in the second way by the use of the construction of the Levi function. Also, in this work, we define a multi meta-φ-monogenic function of first class with the help of the Clifford type algebras depending on parameters.

Año de publicación:

2017

Keywords:

• Clifford algebras
• Clifford type algebras depending on parameters
• Multi meta-φ-monogenic function
• Metamonogenic function
• Multi-meta-monogenic function
• Monogenic function

Fuente:

google

scopus