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Theory of Integral Operators in Parametric Clifford Type Algebras

Abstract:

We develop a theory of integral operators in the Clifford type associative algebra depending on parameters, generated by the structure relations: eiej+ejei=-2Bij,for i, j= 1 , 2 , … , n, where the Bij are the entries of a symmetric and positive definite matrix B∈ Rn×n. As applications we consider some Dirichlet boundary problems for the Dirac operator D in this algebra and the elliptic operator Δ ~ n= div(B∇).