Biorthogonal Wavelets on Vilenkin Groups
Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 110-124 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe algorithms for constructing biorthogonal wavelet systems and refinable functions whose masks are generalized Walsh polynomials. We give new examples of biorthogonal compactly supported wavelets on Vilenkin groups.
@article{TRSPY_2009_265_a8,
     author = {Yu. A. Farkov},
     title = {Biorthogonal {Wavelets} on {Vilenkin} {Groups}},
     journal = {Informatics and Automation},
     pages = {110--124},
     year = {2009},
     volume = {265},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a8/}
}
TY  - JOUR
AU  - Yu. A. Farkov
TI  - Biorthogonal Wavelets on Vilenkin Groups
JO  - Informatics and Automation
PY  - 2009
SP  - 110
EP  - 124
VL  - 265
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a8/
LA  - ru
ID  - TRSPY_2009_265_a8
ER  - 
%0 Journal Article
%A Yu. A. Farkov
%T Biorthogonal Wavelets on Vilenkin Groups
%J Informatics and Automation
%D 2009
%P 110-124
%V 265
%U http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a8/
%G ru
%F TRSPY_2009_265_a8
Yu. A. Farkov. Biorthogonal Wavelets on Vilenkin Groups. Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 110-124. http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a8/

[1] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha: Teoriya i primeneniya, 2-e izd., Izd-vo LKI, M., 2008

[2] Schipp F., Wade W. R., Simon P., Walsh series: An introduction to dyadic harmonic analysis, Adam Hilger, New York, 1990 | MR | Zbl

[3] Golubov B. I., Elementy dvoichnogo analiza, MGUP, M., 2005 | MR

[4] Lang W. C., “Orthogonal wavelets on the Cantor dyadic group”, SIAM J. Math. Anal., 27 (1996), 305–312 | DOI | MR | Zbl

[5] Lang W. C., “Fractal multiwavelets related to the Cantor dyadic group”, Intern. J. Math. and Math. Sci., 21 (1998), 307–314 | DOI | MR | Zbl

[6] Lang W. C., “Wavelet analysis on the Cantor dyadic group”, Houston J. Math., 24 (1998), 533–544 | MR | Zbl

[7] Farkov Yu. A., “Orthogonal $p$-wavelets on $\mathbb R_+$”, Wavelets and splines, Proc. Intern. Conf. (July 3–8, 2003, St. Petersburg, Russia), St. Petersburg State Univ., St. Petersburg, 2005, 4–26 | MR | Zbl

[8] Farkov Yu. A., “Ortogonalnye veivlety s kompaktnymi nositelyami na lokalno kompaktnykh abelevykh gruppakh”, Izv. RAN. Ser. mat., 69:3 (2005), 193–220 | DOI | MR | Zbl

[9] Protasov V. Yu., Farkov Yu. A., “Diadicheskie veivlety i masshtabiruyuschie funktsii na polupryamoi”, Mat. sb., 197:10 (2006), 129–160 | DOI | MR | Zbl

[10] Farkov Yu. A., “Ortogonalnye veivlety na pryamykh proizvedeniyakh tsiklicheskikh grupp”, Mat. zametki, 82:6 (2007), 934–952 | DOI | MR | Zbl

[11] Benedetto J. J., Benedetto R. L., “A wavelet theory for local fields and related groups”, J. Geom. Anal., 14 (2004), 423–456 | DOI | MR | Zbl

[12] Dobeshi I., Desyat lektsii po veivletam, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001

[13] Novikov I. Ya., Protasov V. Yu., Skopina M. A., Teoriya vspleskov, Fizmatlit, M., 2006

[14] Kozyrev S. V., “Teoriya vspleskov kak $p$-adicheskii spektralnyi analiz”, Izv. RAN. Ser. mat., 66:2 (2002), 149–158 | DOI | MR | Zbl

[15] Khrennikov A. Yu., Shelkovich V. M., Skopina M., $p$-Adic refinable functions and MRA-based wavelets, E-print , 2007 arXiv: 0711.2820v1

[16] Farkov Yu. A., “Multiresolution analysis and wavelets on Vilenkin groups”, Facta Univ. Ser. Electron. and Energ., 21:3 (2008), 309–325 | DOI

[17] Farkov Yu. A., “Biortogonalnye diadicheskie veivlety na $\mathbb R_+$”, UMN, 62:6 (2007), 189–190 | DOI | MR | Zbl

[18] Farkov Yu. A., “On wavelets related to the Walsh series”, J. Approx. Theory (to appear) | MR

[19] Soardi P. M., “Biorthogonal $M$-channel compactly supported wavelets”, Constr. Approx., 16 (2000), 283–311 | DOI | MR | Zbl

[20] Bratteli O., Jorgensen P. E. T., “Wavelet filters and infinite-dimensional unitary groups”, Wavelet analysis and applications, AMS/IP Stud. Adv. Math., 25, Amer. Math. Soc., Providence, RI, 2002, 35–65 | MR | Zbl

[21] Maksimov A. Yu., Stroganov S. A., “O primenenii diadicheskikh veivletov dlya szhatiya izobrazhenii”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tez. dokl. 14-i Saratov. zimn. shk., posv. pamyati akad. P. L. Ulyanova, Izd-vo Saratov. un-ta, Saratov, 2008, 108–109