Displaying similar documents to “Representations of semi direct products of groups”

Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform

Eugenio Hernández, Hrvoje Šikić, Guido Weiss, Edward Wilson (2010)

Colloquium Mathematicae

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We just published a paper showing that the properties of the shift invariant spaces, ⟨f⟩, generated by the translates by ℤⁿ of an f in L²(ℝⁿ) correspond to the properties of the spaces L²(𝕋ⁿ,p), where the weight p equals [f̂,f̂]. This correspondence helps us produce many new properties of the spaces ⟨f⟩. In this paper we extend this method to the case where the role of ℤⁿ is taken over by locally compact abelian groups G, L²(ℝⁿ) is replaced by a separable Hilbert space on which a unitary...

Subnormal operators, cyclic vectors and reductivity

Béla Nagy (2013)

Studia Mathematica

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Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.

The duality theorems. Cyclic representations Langlands conjectures

Janusz Szmidt

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CONTENTSIntroduction...................................................................................................... 5Chapter I. Invariant kernels on locally compact groups and cyclicrepresentations....................................................................................................... 8 1. Distributions on topological groups.......................................... 8 2. Invariant kernels and cyclic representations.................................... 9 3. Generalized...

Uniformly cyclic vectors

Joseph Rosenblatt (2006)

Colloquium Mathematicae

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A group acting on a measure space (X,β,λ) may or may not admit a cyclic vector in L ∞ ( X ) . This can occur when the acting group is as big as the group of all measure-preserving transformations. But it does not occur, even though there is no cardinality obstruction to it, for the regular action of a group on itself. The connection of cyclic vectors to the uniqueness of invariant means is also discussed.