Geodesic
On biorthogonal $p$-adic wavelet bases
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 67-83 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Dual $p$-adic multiresolution analyses (MRAs) generated by scaling test functions are studied. It is proved that if two MRAs are dual, then each of MRAs is the Haar MRA. A characterization of all biorthogonal wavelet systems associated with the Haar MRA is given for the case $p=2$. 
@article{ZNSL_2017_455_a6,
     author = {E. J. King and M. A. Skopina},
     title = {On biorthogonal $p$-adic wavelet bases},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--83},
     year = {2017},
     volume = {455},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a6/}
}
TY  - JOUR
AU  - E. J. King
AU  - M. A. Skopina
TI  - On biorthogonal $p$-adic wavelet bases
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 67
EP  - 83
VL  - 455
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a6/
LA  - ru
ID  - ZNSL_2017_455_a6
ER  - 
%0 Journal Article
%A E. J. King
%A M. A. Skopina
%T On biorthogonal $p$-adic wavelet bases
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 67-83
%V 455
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a6/
%G ru
%F ZNSL_2017_455_a6
E. J. King; M. A. Skopina. On biorthogonal $p$-adic wavelet bases. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 67-83. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a6/

[1] S. Albeverio, S. Evdokimov, M. Skopina, “$p$-Adic multiresolution analysis and wavelet frames”, J. Fourier Anal. Appl., 16:5 (2010), 693–714 | DOI | MR | Zbl

[2] S. Albeverio, S. Evdokimov, M. Skopina, “$p$-adic nonorthogonal wavelet bases”, Proceedings of the Steklov Institute of Mathematics, 265 (2009), 1–12 | DOI | MR | Zbl

[3] J. J. Benedetto, R. L. Benedetto, “A wavelet theory for local fields and related groups”, J. Geom. Anal., 3 (2004), 423–456 | DOI | MR | Zbl

[4] B. Behera, O. Jahan, “Multiresolution analysis on local fields and characterization of scaling functions”, Adv. Pure Appl. Math., 3:2 (2012), 181–202 | DOI | MR | Zbl

[5] S. Evdokimov, “Kratnomasshtabnyi analiz i bazisy Khaara na koltse ratsionalnykh adelei”, Zap. nauchn. sem. POMI, 400, 2012, 158–165 | MR

[6] S. Evdokimov, “On non-compactly supported $p$-adic wavelets”, J. Math. Anal. Appl., 443:2 (2016), 1260–1266 | DOI | MR | Zbl

[7] S. Evdokimov, M. Skopina, “On orthogonal $p$-adic wavelet bases”, J. Math. Anal. Appl., 424:2 (2015), 952–965 | DOI | MR | Zbl

[8] S. A. Evdokimov, M. A. Skopina, “2-adicheskie bazisy vspleskov”, Tr. IMM UrO RAN, 15, no. 1, 2009, 135–146

[9] S. Mallat, Multiresolution representation and wavelets, Ph. D. Thesis, University of Pennsylvania, Philadelphia, PA, 1988

[10] Y. Meyer, Ondelettes et fonctions splines, Séminaire EDP, Paris, Décembre 1986

[11] S. V. Kozyrev, “Wavelet analysis as a $p$-adic spectral analysis”, Izvestia Akademii Nauk Seria Math., 66:2 (2002), 149–158 | DOI | MR | Zbl

[12] S. V. Kozyrev, “$p$-Adic pseudodifferential operators and $p$-adic wavelets”, Theor. Math. Physics, 138:3 (2004), 322–332 | DOI | MR | Zbl

[13] A. Yu. Khrennikov, V. M. Shelkovich, “Non-Haar $p$-adic wavelets and their application to pseudo-differential operators and equations”, Appl. Comput. Harmon. Anal., 28:1 (2010), 1–23 | DOI | MR | Zbl

[14] V. M. Shelkovich, M. Skopina, “$p$-Adic Haar multiresolution analysis and pseudo-differential operators”, J. Fourier Anal. Appl., 15:3 (2009), 366–393 | DOI | MR | Zbl

[15] A. Yu. Khrennikov, V. M. Shelkovich, M, Skopina, “$p$-Adic refinable functions and MRA-based wavelets”, J. Approx. Theory, 161 (2009), 226–238 | DOI | MR | Zbl

[16] A. Yu. Khrennikov, V. M. Shelkovich, M. Skopina, “$p$-Adic orthogonal wavelet bases. $p$-Adic Numbers”, Ultrametric Analysis and Applications, 1:2 (2009), 145–156 | MR | Zbl

[17] W. C. Lang, “Orthogonal wavelets on the Cantor dyadic group”, SIAM J. Math. Anal., 27:1 (1996), 305–312 | DOI | MR | Zbl

[18] I. Ya. Novikov, V. Yu. Protasov, M. A. Skopina, Wavelet Theory, Translations Mathematical Monographs, 239, AMS, 2011 | MR | Zbl

[19] L. Pontryagin, Topological Groups, Princeton University Press, Princeton, 1946 | MR

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

[21] J.-P. Serre, Linear representations of finite groups, Graduate Texts in Mathematics, 42, Springer-Verlag, New York–Heidelberg–Berlin, 1977 | DOI | MR | Zbl

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

[23] V. S. Vladimirov, I. V. Volovich, E. I. Zelenov, $p$-Adic analysis and mathematical physics, World Scientific, Singapore, 1994 | MR | Zbl