TY - JOUR
T1 - Classical Fourier Analysis over Homogeneous Spaces of Compact Groups
JO - Analysis in Theory and Applications
VL - 4
SP - 339
EP - 354
PY - 2016
DA - 2016/10
SN - 32
DO - http://doi.org/10.4208/ata.2016.v32.n4.3
UR - https://global-sci.org/intro/article_detail/ata/4675.html
KW - Compact group, homogeneous space, dual space, Fourier transform, Plancherel (trace) formula, Peter-Weyl Theorem.
AB - <p style="text-align: justify;">This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let $G$ be a compact group and $H$ 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 the Weil&#39;s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space $L^2(G/H,\mu)$.</p>