# Abstract Poisson summation formulas over homogeneous spaces of compact groups

Analysis and Mathematical Physics

pp 1–16

First Online: 18 November 2016Received: 12 June 2016Revised: 03 November 2016Accepted: 09 November 2016

Abstract

This paper presents the abstract notion of Poisson summation formulas for homogeneous spaces of compact groups. Let G be a compact group, H be a closed subgroup of G, and \\mu \ be the normalized G-invariant measure over the left coset space G - H associated to the Weil’s formula. We prove that the abstract Fourier transform over G - H satisfies a generalized version of the Poisson summation formula.

KeywordsCompact group Homogeneous space Dual homogeneous space Fourier transform Plancherel trace formula Inversion formula Poisson summation formula Mathematics Subject ClassificationPrimary 20G05 43A85 Secondary 43A30 43A90  Download fulltext PDF

Author: Arash Ghaani Farashahi