Spectral Invariance of $$*$$-Representations of Twisted Convolution Algebras with Applications in Gabor Analysis

Abstract We show spectral invariance for faithful $$*$$ ? -representations a class of twisted convolution algebras. More precisely, if G is locally compact group with continuous 2-cocycle c which the corresponding Mackey $$G_c$$ G c $$C^*$$ C -unique and symmetric, then algebra $$L^1 (G,c)$$ L 1 ( , ) spectrally invariant in $${\mathbb {B}}({\mathcal {H}})$$ B H any -representation as bounded operators on Hilbert space $${\mathcal {H}}$$ . As an application this result we give proof statement that $$\Delta $$ ? closed cocompact subgroup phase abelian $$G'$$ ? , g some function Feichtinger $$S_0 (G')$$ S 0 generates Gabor frame $$L^2 2 over both canonical dual atom tight associated to are also do without use periodization techniques from analysis.