Examples of wavelets for local fields

By Robert L. Benedetto. 2003

88 citations recorded by the source corpus.

Using the wavelet theory introduced by the author and J. Benedetto, we present examples of wavelets on p-adic fields and other locally compact abelian groups with compact open subgroups. We observe that in this setting, the Haar and Shannon wavelets (which are at opposite extremes over the real numbers) coincide and are localized both in time and in frequency. We also study the behavior of the translation operators required in the theory.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fc45a545d1021eb9a583a7cb4aa7d7fb5b0181eb

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

p-Adic Multiresolution Analysis and Wavelet Frames (2008, background): “Benedetto [2, 3 ], however, discussed if it is possible to construct other p-adic wavelets with the same set of translations.”
p-Adic mathematical physics: the first 30 years (2017, methodology): “Important contributions in p-adic wavelet theory were done also by Albeverio, Benedetto, Khrennikov, Shelkovich, Skopina, Evdokimov [41, 42, 6, 7, 143, 144, 222, 145, 15].”