Almansi-Type Decomposition Theorem for Bi-k-regular Functions in the Clifford Algebra Cl _2n+2;0(ℝ)

Abstract

Almansi-type decomposition theorem for bi-k-regular functions defined in a star-like domain Ω ⊆ ℝ ⁿ⁺¹ × ℝ ⁿ⁺¹ centered at the origin with values in the Clifford algebra Cl _2n+2,0(ℝ) is proved. As a corollary, Almansi-type decomposition theorem for biharmonic functions of degree k is given.

Keywords

Real Clifford analysis / Biregular functions / Bi-k-regular functions / Almansi-type decomposition theorem

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