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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

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Inequalities for nonuniform wavelet frames

Firdous A. ShahORCID iD: https://orcid.org/0000-0001-8461-869X
Published Online: 2019-05-16 | DOI: https://doi.org/10.1515/gmj-2019-2026


Gabardo and Nashed studied nonuniform wavelets by using the theory of spectral pairs for which the translation set Λ={0,r/N}+2 is no longer a discrete subgroup of but a spectrum associated with a certain one-dimensional spectral pair. In this paper, we establish three sufficient conditions for the nonuniform wavelet system {ψj,λ(x)=(2N)j/2ψ((2N)jx-λ),j,λΛ} to be a frame for L2(). The proposed inequalities are stated in terms of Fourier transforms and hold without any decay assumptions on the generator of such a system.

Keywords: Nonuniform wavelets; wavelet frame; spectral pairs; Fourier transform

MSC 2010: 42C15; 42C40; 65T60; 42A38; 42A55


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About the article

Received: 2017-04-17

Revised: 2018-01-10

Accepted: 2018-01-15

Published Online: 2019-05-16

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2026.

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