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@article{TM_2009_265_a8, author = {Yu. A. Farkov}, title = {Biorthogonal {Wavelets} on {Vilenkin} {Groups}}, journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova}, pages = {110--124}, publisher = {mathdoc}, volume = {265}, year = {2009}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TM_2009_265_a8/} }
Yu. A. Farkov. Biorthogonal Wavelets on Vilenkin Groups. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 110-124. http://geodesic.mathdoc.fr/item/TM_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