Results 91 to 100 of about 5,385,866 (129)

Graphs with Contours in Multiresolution Analysis on Vilenkin Groups

Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2016
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Step wavelets on Vilenkin groups

Journal of Mathematical Sciences, 2022
The construction of wavelets on the locally compact Vilenkin groups (\(G_p\)) is proposed using multiresolution analysis. The latter is generated by a scaling function which is a solution of a refinement equation. Interestingly, this allows the construction of wavelets (on \(G_p\)), which are band-limited and compactly supported. Note that for wavelets
Maria Skopina
exaly   +3 more sources

Generalized Vilenkin Groups

Mathematical Notes
It is well known that the Vilenkin group \(V_p\) is associated with the cyclic group \(\mathbb{Z}_p\). The authors generalize the group \(V_p\) by replacing \(\mathbb{Z}_p\) with a finite Abelian group \(G\). A description of characters for such groups is given, a Haar type system is defined, and the corresponding Walsh type functions are introduced ...
Vodolazov, A. M., Skopina, M. A.
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Algorithms for wavelet construction on Vilenkin groups

P-Adic Numbers, Ultrametric Analysis, and Applications, 2011
Let \(G_p\) be the \(p\)-adic Vilenkin group. In this paper the authors obtain some algorithms for constructing orthogonal and biorthogonal compactly supported wavelets on \(G_p\). In his series of previous papers [Math. Notes 82, No. 6, 843--859 (2007); translation from Mat. Zametki 82, No. 6, 934--952 (2007; Zbl 1142.42015); J. Approx. Theory 161, No.
Farkov, Yuri A., Rodionov, Evgeny A.
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Calculus on Walsh and Vilenkin Groups

2015
The usual concept of differentiation is not suitable for functions which are locally constant. So it can not be used either in the study of Walsh-Fourier series as with trigonometric series. However, Gibbs [16], Butzer and Wagner [2] introduced the concept of dyadic derivative which satisfies some of the usual properties of the differentiation, but not
György Gát, Rodolfo Toledo
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Biorthogonal wavelets on Vilenkin groups

Proceedings of the Steklov Institute of Mathematics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Periodic wavelets on the p-adic Vilenkin group

P-Adic Numbers, Ultrametric Analysis, and Applications, 2011
Let \((G,\oplus)\) be the locally compact \(p\)-adic Vilenkin group, \(U_0\) the unit ball, \(A\) the dilation operator and \(U_n=A^{-n}U_0\), \((w_l)_{l=0}^\infty\) Vilenkin functions. Using the modified Vilenkin-Dirichlet kernel \[ D_n^*(x):=\alpha+\sum_{k=1}^{N-l}w_k(x)+\alpha w_{N-1}(x), \] the author introduces the functions \[ \begin{multlined ...
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Orthonormal systems on Vilenkin groups

Acta Mathematica Hungarica, 1991
Let \(G_ m\) denote the topological product of a sequence of discrete cyclic groups \(Z_{m_ k}\) \((k\geq 0,m_ k\geq 2)\), with the direct product measure \(\mu\) given by the pointwise measures \(\mu_ k\) for which \(\mu_ k(j)=1/m_ k\) \((j\in Z_{m_ k})\). Starting with a certain particular complete and orthonormal system of characters \(\psi_ 0,\psi_
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Dirichlet sets in Vilenkin groups

Acta Mathematica Hungarica, 1993
The author proves that every Dirichlet set in a compact Vilenkin group \(G\) is a strong set of uniqueness. This generalizes a similar theorem for such sets in the dyadic group, due to \textit{K. Yoneda} [Tôhoku Math. J., II. Ser. 38, 1-14 (1986; Zbl 0603.42026)]. Furthermore, the author presents some sufficient conditions for a subset of \(G\) to be a
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Orthogonal and Periodic Wavelets on Vilenkin Groups

2019
As noted in Chap. 1, the Walsh function can be identified with characters of the Cantor dyadic group. This fact was first recognized by Gelfand in the 1940s, who offered to Vilenkin study series with respect to characters of a large class of abelian groups which includes the Cantor group as special case see Vilenkin [1], Fine [2], Agaev, Vilenkin ...
Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi   +2 more
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