Abstract Poisson summation formulas over homogeneous spaces of compact groups

作者：Farashahi Arash Ghaani^*

来源：Analysis and Mathematical Physics, 2017, 7(4): 493-508.

DOI：10.1007/s13324-016-0156-2

• Compact group
• Homogeneous space
• Dual homogeneous space
• Fourier transform
• Plancherel (trace) formula
• Inversion formula
• Poisson summation formula

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 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.

• 出版日期2017-12