Spectral Invariance of $$*$$-Representations of Twisted Convolution Algebras with Applications in Gabor Analysis
Spectral Invariance of $$*$$-Representations of Twisted Convolution Algebras with Applications in Gabor Analysis
Abstract We show spectral invariance for faithful $$*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:math> -representations for a class of twisted convolution algebras. More precisely, if G is a locally compact group with a continuous 2-cocycle c for which the corresponding Mackey group $$G_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>c</mml:mi> …