Abstract
In this article, we construct a Riesz multiresolution analysis (MRA) on locally compact Abelian groups (LCA) starting from a suitably given scaling function. Subsequently, we investigate all the conditions under which a scaling function generates a Riesz MRA for \(L^{2}(G)\). Besides, all the results are braced with illustrative examples. Towards the culmination, several exceptions are discussed regarding the nonexistence of dilative automorphism \(\alpha\) of \(G\).
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Funding
The first author is financially supported by HRDG-CSIR, Government of India, grant no. 09/045 (1653)/2019-EMR-I.
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Satyapriya, Kumar, R. & Shah, F.A. Riesz Multiresolution Analysis on Locally Compact Abelian Groups: Construction and Exceptions. J. Contemp. Mathemat. Anal. 58, 125–135 (2023). https://doi.org/10.3103/S1068362323020085
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DOI: https://doi.org/10.3103/S1068362323020085