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PERTURBATION OF WAVELET FRAMES AND RIESZ BASES I
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 Title & Authors
PERTURBATION OF WAVELET FRAMES AND RIESZ BASES I
Lee, Jin; Ha, Young-Hwa;
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 Abstract
Suppose that generates a wavelet frame (resp. Riesz basis) with bounds A and B. If satisfies $\^{\psi}(\xi)\;\^{\phi}(\xi){\;}<{\;}{\lambda}\frac{\xi^{\alpha}}{(1+\xi)^{\gamma}}$ for some positive constants such that $1{\;}<1{\;}+{\;}\alpha{\;}<{\;}\gamma{\;}and{\;}{\lambda}^2M{\;}<{\;}A$, then also generates a wavelet frame (resp. Riesz basis) with bounds , where M is a constant depending only on the dilation step a, and the translation step b.
 Keywords
wavelet;frame;Riesz basis;perturbation;stability;
 Language
English
 Cited by
 References
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Appl. Comput. Harmon. Anal., vol.2. pp.160-173 crossref(new window)

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An Introduction to Nonharmonic Fourier Series,