Frames in Walsh analysis, Hadamard matrices, and uniformly distributed sets

Yu. A. Farkov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 17-30.

Résumé

This paper continues the author's works on the relationship of Walsh analysis with recent results in the theory of orthogonal wavelet bases and the theory of tight frames. Parametric sets for orthogonal wavelets and compactly supported Parseval frames on Vilenkin groups are defined. Methods for constructing equiangular tight frames through Hadamard matrices are described. Also, we note that finite tight frames associated with Walsh functions can be useful for detecting hidden regular structures of uniformly distributed point sets.

Détail

Mots-clés : Hadamard matrix
Keywords: Walsh function, Steiner system, wavelet, equiangular tight frame, uniformly distributed set, Vilenkin group.

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