Cyclic Subspaces for Unitary Representations of Lca Groups: Generalized Zak Transform
نویسندگان
چکیده
Date: September 2, 2008. 2000 Mathematics Subject Classification. 42C40, 43A65,43A70.
منابع مشابه
The Zak Transform and the Structure of Spaces Invariant by the Action of an Lca Group
We study closed subspaces of L(X ), where (X , μ) is a σ-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group Γ on X . We provide a complete description for these spaces in terms of range functions and a suitable generalized Zak transform. As an application of our main result, we prove a characterization of...
متن کاملImportance of Zak Transforms for Harmonic Analysis
In engineering and applied mathematics, Zak transforms have been effectively used for over 50 years in various applied settings. As Gelfand observed in a 1950 paper, the variable coefficient Fourier series ideas articulated in Andre Weil’s famous book on integration lead to an exceedingly elementary proof of the Plancherel Theorem for LCA groups. The transform for functions on R appearing in Za...
متن کاملOn local gamma factors for orthogonal groups and unitary groups
In this paper, we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for irreducible admissible representations of orthogonal groups, or unitary groups. One family is that of local integrals of the doubling method, and the other family is that of local integrals expressed in terms of sph...
متن کاملSome bounds on unitary duals of classical groups - non-archimeden case
We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups. Roughly, they can show up only if the central character of the inducing irreducible cuspidal representation is dominated by the square root of the modular character of the minimal parabolic subgroup. For unitarizable subquotients...
متن کاملThe Zak transform and sampling theorems for wavelet subspaces
The Zak transform is used for generalizing a sampling theorem of G. Walter for wavelet subspaces. Cardinal series based on signal samples f(a + n), n E 2 with a possibly unequal to 0 (Walter’s case) are considered. The condition number of the sampling operator and worst-case aliasing errors are expressed in terms of Zak transforms of scaling function and wavelet. This shows that the stability o...
متن کامل