Dual wavelets associated with nonuniform MRA

  • Mohd Younus Bhat Department of Mathematics National Institute of Technology Srinagar, Jammu and Kashmir, India.
Keywords: Nonuniform, Biorthogonal, Scaling function, Fourier transform

Abstract

A generalization of Mallats classical multiresolution analysis, based on thetheory of spectral pairs, was considered in two articles by Gabardo and Nashed. In thissetting, the associated translation set is no longer a discrete subgroup of R but a spectrumassociated with a certain one-dimensional spectral pair and the associated dilation is aneven positive integer related to the given spectral pair. In this paper, we construct dualwavelets which are associated with Nonuniform Multiresolution Analysis. We show thatif the translates of the scaling functions of two multiresolution analyses are biorthogonal,then the associated wavelet families are also biorthogonal. Under mild assumptions onthe scaling functions and the wavelets, we also show that the wavelets generate Rieszbases

Author Biography

Mohd Younus Bhat, Department of Mathematics National Institute of Technology Srinagar, Jammu and Kashmir, India.
Department of Mathematics National Institute of Technology Srinagar, Jammu and Kashmir, India.

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Published
2019-06-30
How to Cite
Bhat, M. Y. (2019). Dual wavelets associated with nonuniform MRA. Tamkang Journal of Mathematics, 50(2), 119-132. https://doi.org/10.5556/j.tkjm.50.2019.2646
Section
Papers