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http://dx.doi.org/10.5666/KMJ.2021.61.2.371

Riesz and Tight Wavelet Frame Sets in Locally Compact Abelian Groups  

Sinha, Arvind Kumar (Department of Mathematics, National Institute of Technology Raipur)
Sahoo, Radhakrushna (Department of Mathematics, National Institute of Technology Raipur)
Publication Information
Kyungpook Mathematical Journal / v.61, no.2, 2021 , pp. 371-381 More about this Journal
Abstract
In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L2(G) and, using the scaling function, we construct an orthonormal wavelet basis for L2(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.
Keywords
wavelet frame sets; Riesz wavelets; tight wavelet frame sets; translational and multiplicative tilings; spectral set;
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