Czasopismo
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Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
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Rocznik
Tom
Numer
Strony
313-332
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
autor
- Department of Mathematics, University of Zagreb, Bijenička 30, HR-10 000 Zagreb, Croatia
autor
- Department of Mathematics, Washington University, Box 1146, St. Louis, MO 63130, U.S.A.
autor
- Department of Mathematics, Washington University, Box 1146, St. Louis, MO 63130, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-1-17