arXiv subjects

Wolfgang Palzer

Publications and source records attributed to Wolfgang Palzer.

3 recordsLinked to original sources

arXiv2016

Non-Euclidean Fourier inversion on super-hyperbolic space

For the super-hyperbolic space in any dimension, we introduce the non-Euclidean Helgason--Fourier transform. We prove an inversion formula exhibiting residue contributions at the poles of the Harish-Chandra c-function, signalling discrete parts in the spectrum. The proof is based on a detailed study of the spherical superfunctions, using recursion relations and localization techniques to normalize them precisely, careful estimates of their derivatives, and a rigorous analysis of the boundary terms appearing in the polar coordinate expression of the invariant integral

math.RT↗

arXiv2014

Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces

We compute the Harish-Chandra $c$-function for a generic class of rank-one purely non-compact Riemannian symmetric superspaces $X=G/K$ in terms of Euler $Γ$ functions, proving that it is meromorphic. Compared to the even case, the poles of the $c$-function are shifted into the right half-space. We derive the full asymptotic Harish-Chandra series expansion of the spherical superfunctions on $X$. In the case where the multiplicity of the simple root is an even negative number, they have a closed expression as Jacobi polynomials for an unusual choice of parameters.

math.RT↗

arXiv2011

Integration on Non-Compact Supermanifolds

We investigate the Berezin integral of non-compactly supported quantities. In the framework of supermanifolds with corners, we give a general, explicit and coordinate-free repesentation of the boundary terms introduced by an arbitrary change of variables. As a corollary, a general Stokes's theorem is derived - here, the boundary integral contains transversal derivatives of arbitrarily high order.

math.DG↗