Laurent expansion and \(L_2\)-boundary values in Hermitian Clifford analysis. (English) Zbl 07930077
Summary: Inspired by the classical Cauchy transform in \(L_2(\partial B(R))\), we first derive the Laurent expansion for Hermitian monogenic functions in Hermitian Clifford analysis, and we obtain direct applications of this expansion. Then we use the Laurent expansion to study the \(L_2\)-boundary values of Hermitian monogenic functions, we prove that every \(f\in L_2(S^{2m - 1}; V)\) can be decomposed as a sum of boundary values of functions, which are \(h\)-monogenic inside and outside the unit ball respectively.
MSC:
| 30G35 | Functions of hypercomplex variables and generalized variables |
| 15A66 | Clifford algebras, spinors |
| 30B10 | Power series (including lacunary series) in one complex variable |
Keywords:
Hermitian Clifford analysis; Hermitian monogenic; Laurent expansion; Cauchy transform; \(L_2\) boundary valueReferences:
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