p-Adic Multiresolution Analysis and Wavelet Frames

Albeverio, S., Khrennikov, A.Yu., Shelkovich, V.M.: Harmonic analysis in the p-adic Lizorkin spaces: fractional operators, pseudo-differential equations, p-adic wavelets, Tauberian theorems. J. Fourier Anal. Appl. 12(4), 393–425 (2006)

Benedetto, J.J., Benedetto, R.L.: A wavelet theory for local fields and related groups. J. Geom. Anal. 3, 423–456 (2004)

Benedetto, R.L.: Examples of wavelets for local fields. In: Wavelets, Frames and Operator Theory. Contemp. Math., vol. 345, pp. 27–47. Am. Math. Soc., Providence (2004)

de Boor, C., DeVore, R., Ron, A.: On construction of multivariate (pre) wavelets. Constr. Approx. 9, 123–166 (1993)

Dahlke, S.: Multiresolution analysis and wavelets on locally compact abelian groups. In: Laurent, P.-J., Le Méhanté, A., Schumaker, L.L. (eds.) Wavelets, Images, and Surface Fitting. AK Peters, Wellesley (1994)

Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSR Series in Appl. Math. SIAM, Philadelphia (1992)

Fornasier, M.: Quasi-orthogonal decompositions of structured frames. J. Math. Anal. Appl. 289(1), 180–199 (2004)

Gelfand, I.M., Graev, M.I., Pyatetskii-Shapiro, I.I.: Representation Theory and Automorphic Functions, Generalized Functions, vol. 6. Nauka, Moscow (1966)

Gröchenig, K., Madych, W.R., Skvortsov, V.: Multiresolution analysis, Haar bases, and self-similar tilings of ℝ n . IEEE Trans. Inform. Theory 38, 556–568 (1992)

Katok, S.: p-Adic Analysis Compared with Real. Princeton University Press, Princeton (1975)

Khrennikov, A.Yu.: Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models. Kluwer, Dordrecht (1997)

Khrennikov, A.Yu.: Information Dynamics in Cognitive, Psychological, Social, and Anomalous Phenomena. Fundamental Theories of Physics. Kluwer, Dordrecht (2004)

Khrennikov, A.Yu., Shelkovich, V.M.: p-Adic multidimensional wavelets and their application to p-adic pseudo-differential operators (2006). http://arxiv.org/abs/math-ph/0612049

Khrennikov, A.Yu., Shelkovich, V.M.: Non-Haar p-adic wavelets and their application to pseudo-differential operators and equations. Appl. Comput. Harmon. Anal. 28(1), 1–23 (2009)

Khrennikov, A.Yu., Shelkovich, V.M.: An infinite family of p-adic non-Haar wavelet bases and pseudo-differential operators. P-Adic Numb. Ultrametr. Anal. Appl. 1(3), 204–216 (2009)

Khrennikov, A.Yu., Shelkovich, V.M., Skopina, M.: p-Adic refinable functions and MRA-based wavelets. J. Approx. Theory 161, 226–238 (2009)

Kozyrev, S.V.: Wavelet analysis as a p-adic spectral analysis. Izv. Akad. Nauk, Ser. Mat. 66(2), 149–158 (2002)

Kozyrev, S.V.: p-Adic pseudodifferential operators and p-adic wavelets. Theor. Math. Phys. 138(3), 1–42 (2004)

Lang, S.: Algebra. Graduate Texts in Mathematics, vol. 211. Springer, Berlin (2002)

Lang, W.C.: Orthogonal wavelets on the Cantor dyadic group. SIAM J. Math. Anal. 27, 305–312 (1996)

Lang, W.C.: Wavelet analysis on the Cantor dyadic group. Houston J. Math. 24, 533–544 (1998)

Lang, W.C.: Fractal multiwavelets related to the cantor dyadic group. Int. J. Math. Math. Sci. 21(2), 307–314 (1998)

Lemarié, P.G.: Bases d’ondelettes sur les groupes de Lie stratifiés. Bull. Math. Soc. France 117, 211–233 (1989)

Mallat, S.: Multiresolution representation and wavelets. Ph.D. thesis, University of Pennsylvania, Philadelphia, PA (1988)

Meyer, Y.: Ondelettes et fonctions splines. Séminaire EDP, Paris, Décembre 1986

Novikov, I.Ya., Protassov, V.Yu., Skopina, M.A.: Wavelet Theory. Fizmatlit, Moscow (2005) (in Russian)

Pontryagin, L.: Topological Groups. Princeton University Press, Princeton (1946)

Protasov, V.Yu., Farkov, Yu.A.: Dyadic wavelets and refinable functions on a half-line. Mat. Sb. 197(10), 129–160 (2006)

Protasov, V.Yu., Farkov, Yu.A.: Sb. Math. 197, 1529–1558 (2006) (English transl.)

Shelkovich, V.M., Skopina, M.: p-Adic Haar multiresolution analysis and pseudo-differential operators. J. Fourier Anal. Appl. 15(3), 366–393 (2009)

Taibleson, M.H.: Fourier Analysis on Local Fields. Princeton University Press, Princeton (1975)

Vladimirov, V.S., Volovich, I.V., Zelenov, E.I.: p-Adic Analysis and Mathematical Physics. World Scientific, Singapore (1994)