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

• Autorzy: Eugenio Hernández , Hrvoje Šikić , Guido Weiss , Edward Wilson
• Języki publikacji: EN

Abstrakty

EN

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 representation of G acts, and the role of L²(𝕋ⁿ,p) is assumed by a weighted space L²(Ĝ,w), where Ĝ is the dual group of G. This provides many different extensions of the theory of wavelets and related methods for carrying out signal analysis.

Kategorie tematyczne

• 42C40: Wavelets and other special systems
• 43A65: Representations of groups, semigroups, etc.
• 43A70: Analysis on specific locally compact and other abelian groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 1
• Strony: 313-332

Daty

wydano

2010

Twórcy

autor

Eugenio Hernández

• Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

autor

Hrvoje Šikić

• Department of Mathematics, University of Zagreb, Bijenička 30, HR-10 000 Zagreb, Croatia

autor

Guido Weiss

• Department of Mathematics, Washington University, Box 1146, St. Louis, MO 63130, U.S.A.

autor

Edward Wilson

• Department of Mathematics, Washington University, Box 1146, St. Louis, MO 63130, U.S.A.

Identyfikatory

DOI

10.4064/cm118-1-17