Integration in superspace using distribution theory

Abstract

In this paper, a new class of Cauchy integral formulae in superspace is obtained, using formal expansions of distributions. This allows to solve five open problems in the study of harmonic and Clifford analysis in superspace.

References in corpus (5)

• Spherical harmonics and integration in superspace
• Fourier transform and related integral transforms in superspace
• Fundamental solutions for the super Laplace and Dirac operators and all their natural powers
• A Clifford analysis approach to superspace
• A Cauchy integral formula in superspace

Cited by in corpus (12)

• Divergence Theorems and the Supersphere
• Orthogonality of Hermite polynomials in superspace and Mehler type formulae
• Orthosymplectically invariant functions in superspace
• The orthosymplectic supergroup in harmonic analysis
• Invariant integration on orthosymplectic and unitary supergroups
• Distributions and Integration in superspace
• A minimal representation of the orthosymplectic Lie supergroup
• Hilbert space for quantum mechanics on superspace
• The Fourier Transform on Quantum Euclidean Space
• Bochner-Martinelli formula in superspace
• Pizzetti and Cauchy formulae for higher dimensional surfaces: a distributional approach
• Fischer decomposition for polynomials on superspace