Wavelets on compact abelian groups

Marcin Bownik; Qaiser Jahan

Wavelets on compact abelian groups

Classical Analysis and ODEs 2020-05-15 v2

Authors: Marcin Bownik , Qaiser Jahan

Abstract

Multiresolution analysis (MRA) on compact abelian group $G$ has been constructed with epimorphism as a dilation operator. We show a characterization of scaling sequences of an MRA on $L^p(G)$ , $1\le p<\infty$ . With the help of this scaling sequence we construct a wavelet orthonormal basis of $L^2(G)$ .

Keywords

wavelet analysis

Cite

@article{arxiv.1903.09194,
  title  = {Wavelets on compact abelian groups},
  author = {Marcin Bownik and Qaiser Jahan},
  journal= {arXiv preprint arXiv:1903.09194},
  year   = {2020}
}

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