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Tr. Mat. Inst. Steklova, 2009, Volume 265, Pages 7–18 (Mi tm818)  

This article is cited in 14 scientific papers (total in 14 papers)

$p$-Adic Nonorthogonal Wavelet Bases

S. Albeverioab, S. Evdokimovc, M. Skopinad

a Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany
b Interdisziplinäres Zentrum für Komplexe Systeme, Universität Bonn, Bonn, Germany
c St. Petersburg Department of the Steklov Institute of Mathematics, Russian Academy of Sciences, St.-Petersburg, Russia
d Faculty of Applied Mathematics and Control Processes, St.-Petersburg State University, St.-Petersburg, Russia

Abstract: A method for constructing MRA-based $p$-adic wavelet systems that form Riesz bases in $L^2(\mathbb Q_p)$ is developed. The method is implemented for an infinite family of MRAs.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 265, 1–12

Bibliographic databases:

UDC: 517.5
Received in October 2008

Citation: S. Albeverio, S. Evdokimov, M. Skopina, “$p$-Adic Nonorthogonal Wavelet Bases”, Selected topics of mathematical physics and $p$-adic analysis, Collected papers, Tr. Mat. Inst. Steklova, 265, MAIK Nauka/Interperiodica, Moscow, 2009, 7–18; Proc. Steklov Inst. Math., 265 (2009), 1–12

Citation in format AMSBIB
\by S.~Albeverio, S.~Evdokimov, M.~Skopina
\paper $p$-Adic Nonorthogonal Wavelet Bases
\inbook Selected topics of mathematical physics and $p$-adic analysis
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2009
\vol 265
\pages 7--18
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2009
\vol 265
\pages 1--12

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    This publication is cited in the following articles:
    1. S. F. Lukomskii, “Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases”, Sb. Math., 201:5 (2010), 669–691  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Lukomskii S.F., “Haar system on a product of zero-dimensional compact groups”, Cent. Eur. J. Math., 9:3 (2011), 627–639  crossref  mathscinet  zmath  isi  elib  scopus
    3. S. F. Lukomskii, “Neortogonalnyi kratnomasshtabnyi analiz na nul-mernykh lokalno kompaktnykh gruppakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:3(1) (2011), 25–32  mathnet  crossref  elib
    4. S. F. Lukomskii, “Haar System on the Product of Groups of $p$-Adic Integers”, Math. Notes, 90:4 (2011), 517–532  mathnet  crossref  crossref  mathscinet  isi
    5. Lukomskii S.F., “Multiresolution analysis on product of zero-dimensional Abelian groups”, J. Math. Anal. Appl., 385:2 (2012), 1162–1178  crossref  mathscinet  zmath  isi  elib  scopus
    6. Khrennikov A.Y. Kosyak A.V. Shelkovich V.M., “Wavelet Analysis on Adeles and Pseudo-Differential Operators”, J. Fourier Anal. Appl., 18:6 (2012), 1215–1264  crossref  mathscinet  zmath  isi  elib  scopus
    7. S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196  mathnet  crossref  crossref  isi  elib  elib
    8. Lukomskii S.F., “Riesz Multiresolution Analysis on Vilenkin Groups”, Dokl. Math., 90:1 (2014), 412–415  crossref  mathscinet  zmath  isi  elib  scopus
    9. S. F. Lukomskii, “Riesz multiresolution analysis on zero-dimensional groups”, Izv. Math., 79:1 (2015), 145–176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Evdokimov S., Skopina M., “on Orthogonal P-Adic Wavelet Bases”, J. Math. Anal. Appl., 424:2 (2015), 952–965  crossref  mathscinet  zmath  isi  elib  scopus
    11. Evdokimov S., “On non-compactly supported p-adic wavelets”, J. Math. Anal. Appl., 443:2 (2016), 1260–1266  crossref  mathscinet  zmath  isi  elib  scopus
    12. Jahan Q., “Characterization of Low-pass Filters on Local Fields of Positive Characteristic”, Can. Math. Bul.-Bul. Can. Math., 59:3 (2016), 528–541  crossref  mathscinet  zmath  isi  scopus
    13. E. J. King, M. A. Skopina, “On biorthogonal $p$-adic wavelet bases”, J. Math. Sci. (N. Y.), 234:2 (2018), 158–169  mathnet  crossref
    14. Dragovich B., Khrennikov A.Yu., Kozyrev S.V., Volovich I.V., Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
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