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Mat. Sb., 2007, Volume 198, Number 11, Pages 135–152 (Mi msb1981)  

This article is cited in 13 scientific papers (total in 13 papers)

Approximation by dyadic wavelets

V. Yu. Protasov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Systems of dyadic wavelets on the positive half-line $\mathbb R_+$ equipped with the operation of binary summation are studied. Several problems concerning approximation properties of such wavelets are solved. In particular, explicit formulae for the order of approximation of smooth functions and of binary-smooth functions on $\mathbb R_+$ (smooth in the dyadic metric on the binary half-line) are obtained. The dyadic approximations with best approximation properties are characterized. The relation between the smoothness of wavelets and their order of approximation is analysed in various function spaces.
Bibliography: 24 titles.


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English version:
Sbornik: Mathematics, 2007, 198:11, 1665–1681

Bibliographic databases:

UDC: 517.518.3+517.518.543+517.965
MSC: 42C40, 41A30
Received: 06.07.2006 and 05.06.2007

Citation: V. Yu. Protasov, “Approximation by dyadic wavelets”, Mat. Sb., 198:11 (2007), 135–152; Sb. Math., 198:11 (2007), 1665–1681

Citation in format AMSBIB
\by V.~Yu.~Protasov
\paper Approximation by dyadic wavelets
\jour Mat. Sb.
\yr 2007
\vol 198
\issue 11
\pages 135--152
\jour Sb. Math.
\yr 2007
\vol 198
\issue 11
\pages 1665--1681

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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. 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
    3. 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
    4. Yu. A. Farkov, “Wavelet Expansions on the Cantor Group”, Math. Notes, 96:6 (2014), 996–1007  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Lukomskii S.F., “Riesz Multiresolution Analysis on Vilenkin Groups”, Dokl. Math., 90:1 (2014), 412–415  crossref  mathscinet  zmath  isi  elib  scopus
    6. 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
    7. S. F. Lukomskii, G. S. Berdnikov, Yu. S. Kruss, “On the Orthogonality of a System of Shifts of the Scaling Function on Vilenkin Groups”, Math. Notes, 98:2 (2015), 339–342  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Yu. S. Kruss, “O tochnosti otsenki chisla shagov algoritma postroeniya masshtabiruyuschei funktsii na lokalnykh polyakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:3 (2015), 279–287  mathnet  crossref  elib
    9. G. S. Berdnikov, “Grafy s konturami v kratnomasshtabnom analize na gruppakh Vilenkina”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:4 (2016), 377–388  mathnet  crossref  mathscinet  elib
    10. Berdnikov G.S., Kruss I.S., Lukomskii S.F., “on Orthogonal Systems of Shifts of Scaling Function on Local Fields of Positive Characteristic”, Turk. J. Math., 41:2 (2017), 244–253  crossref  mathscinet  zmath  isi  elib  scopus
    11. Berdnikov G., Kruss I., Lukomskii S., “How to Construct Wavelets on Local Fields of Positive Characteristic”, Lobachevskii J. Math., 38:4, SI (2017), 615–621  crossref  mathscinet  zmath  isi  scopus
    12. Siddiqi A.H., Manchanda P., “Sampling and Approximation Theorems For Wavelets and Frames on Vilenkin Group”, 2017 International Conference on Sampling Theory and Applications (Sampta), IEEE, 2017, 614–616  crossref  isi
    13. G. S. Berdnikov, “Necessary and sufficient condition for an orthogonal scaling function on Vilenkin groups”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:1 (2019), 24–33  mathnet  crossref  elib
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