Trace Class Groups
Copyright policy )Trace Class Groups
A representation $π$ of a locally compact group $G$ is called \e{trace class}, if for every test function $f$ the induced operator $π(f)$ is a trace class operator. The group $G$ is called \e{trace class}, if every $π\in G$ is trace class. We show that trace class groups are type I and give a criterion for semi-direct products to be trace class and show that a representation $π$ is trace class if and only if $π\otimesπ'$ can be realized in the space of distributions.
Spectral theory; trace formulas (e.g., that of Selberg), Unitary representations of locally compact groups, Induced representations for locally compact groups, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis), type I group, Representation Theory (math.RT), Representations of Lie and linear algebraic groups over real fields: analytic methods, Mathematics - Representation Theory, trace class operator, unitary representation
Spectral theory; trace formulas (e.g., that of Selberg), Unitary representations of locally compact groups, Induced representations for locally compact groups, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis), type I group, Representation Theory (math.RT), Representations of Lie and linear algebraic groups over real fields: analytic methods, Mathematics - Representation Theory, trace class operator, unitary representation
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