LAUSR

Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups Arash Ghaani Farashahi Abstract. _is paper introduces a uniûed operator theory approach to the abstract Plancherel (trace) formulas 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 le coset space of H inG and μ be the normalizedG-invariantmeasure onG/H associated to theWeil’s formula. _en, we present a generalized abstract notion of Plancherel (trace) formula for theHilbert space L(G/H, μ). _is paper introduces a uniûed operator theory approach to the abstract Plancherel (trace) formulas 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 le coset space of H inG and μ be the normalizedG-invariantmeasure onG/H associated to theWeil’s formula. _en, we present a generalized abstract notion of Plancherel (trace) formula for theHilbert space L(G/H, μ).