AB-wavelet frames in L2(Rn) | Zendy

H. M. Srivastava | Zendy; Firdous A. Shah | Zendy

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AB-wavelet frames in L2(Rn)

Author(s) -

H. M. Srivastava,

Firdous A. Shah

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1911587s

Subject(s) - wavelet , mathematics , context (archaeology) , frame (networking) , frame work , realm , pure mathematics , fourier transform , mathematical analysis , artificial intelligence , theoretical physics , computer science , paleontology , telecommunications , physics , political science , law , biology

In order to provide a unified treatment for the continuum and digital realm of multivariate data, Guo, Labate, Weiss and Wilson [Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 78-87] introduced the notion of AB-wavelets in the context of multiscale analysis. We continue and extend their work by studying the frame properties of AB-wavelet systems {DADBTk??(k ? Zn; 1 <? ? <? L)}in L2(Rn). More precisely, we establish four theorems giving su_cient conditions under which the AB-wavelet system constitutes a frame for L2(Rn). The proposed conditions are stated in terms of the Fourier transforms of the generating functions.

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