Bochner-Martinelli formula in superspace
Juan Bory Reyes, Al\'i Guzm\'an Ad\'an, Frank Sommen
TL;DR
This paper extends the classical Bochner-Martinelli formula to superspace within Hermitian Clifford analysis, developing integral formulas for superfunctions and advancing the harmonic and hypercomplex function theory in superspace.
Contribution
It introduces a superspace version of the Bochner-Martinelli formula using projections on spinor-valued superfunctions, expanding the mathematical framework of superspace analysis.
Findings
Established a superspace Bochner-Martinelli formula
Extended classical integral formulas to superspace
Enhanced the theory of harmonic and hypercomplex functions in superspace
Abstract
In a series of recent papers, a harmonic and hypercomplex function theory in superspace has been established and amply developed. In this paper, we address the problem of establishing Cauchy integral formulae in the framework of Hermitian Clifford analysis in superspace. This allows us to obtain a successful extension of the classical Bochner-Martinelli formula to superspace by means of the corresponding projections on the space of spinor-valued superfunctions.
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