Abstract Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups

Canadian mathematical bulletin

Arash Ghaani Farashahi¹ 

[1] Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1 A-1090 Wien, Vienna, Austria

关键词: compact group;    homogeneous space;    dual space;    Plancherel (trace) formula;   

DOI  :  10.4153/CMB-2016-037-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

This paper introduces a unified operator theory approach to theabstract Plancherel (trace) formulas over homogeneous spaces of compact groups. Let $G$ be a compact groupand $H$ be a closed subgroup of $G$. Let $G/H$ be the left coset space of $H$ in $G$ and $mu$ be the normalized $G$-invariant measure on $G/H$ associated to theWeil's formula. Then, we present a generalized abstract notion of Plancherel(trace) formula for the Hilbert space $L^2(G/H,mu)$.

【 授权许可】

Unknown