Multidimensional periodic wavelets

I. E. Maksimenko ; M. A. Skopina

Algebra i analiz, Tome 15 (2003) no. 2, pp. 1-39.

Bibliographie

[1] Daubechies I., Ten lectures on wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math., 61, SIAM, Philadelphia, PA, 1992 | MR | Zbl

[2] Mallat S., “Multiresolution approximations and wavelet orthonormal bases of”, Trans. Amer. Math. Soc., 315 (1989), 69–87 | DOI | MR | Zbl

[3] Meyer Y., Ondelettes et opérateurs. I. Ondelettes, Herman, Paris, 1990 | MR

[4] de Boor C., DeVore R., Ron A., “On the construction of multivariate (pre) wavelets”, Constr. Approx., 9 (1993), 123–166 | DOI | MR | Zbl

[5] Jia R. Q., Micchelli C. A., “Using the refinement equations for the construction of pre-wavelets. II. Powers of two”, Curves and Surfaces (Chamonix-Mont-Blanc, 1990), eds. P. J. Laurent, A. Le Mhauté and L. L. Schumaker, Academic Press, Boston, MA, 1991, 209–246 | MR

[6] Jia R. Q., Micchelli C. A., “Using the refinement equation for the construction of pre-wavelets. V. Extensibility of trigonometric polynomials”, Computing, 48:1 (1992), 61–72 | DOI | MR | Zbl

[7] Riemenschneider S. D., Shen Z. W., “Box splines, cardinal series and wavelets”, Approximation Theory and Functional Analysis (College Station, TX, 1990), ed. C. K. Chui, Academic Press, Boston, MA, 1991, 133–149 | MR

[8] Riemenschneider S. D., Shen Z. W., “Wavelets and pre-wavelets in low dimensions”, J. Approx. Theory, 71:1 (1992), 18–38 | DOI | MR | Zbl

[9] Riemenschneider S. D., Shen Z. W., Construction of compactly supported biorthogondl wavelets in $L_2(\mathbb R^s)$, Preprint, 1997 | MR

[10] Ji H., Riemenschneider S. D., Shen Z. W., Multivariate compactly supported fundamental refinable functions and biorthogonal wavelets, Preprint

[11] Jia R. Q., Shen Z., “Multiresolution and wavelets”, Proc. Edinburgh Math. Soc. (2), 37:2 (1994), 271–300 | DOI | MR | Zbl

[12] Chui C. K., Mhaskar H. N., “On trigonometric wavelets”, Constr. Approx., 9:2–3 (1993), 167–190 | DOI | MR | Zbl

[13] Chui C. K., Wang J., “A general framework of compactly supported splines and wavelets”, J. Approx. Theory, 71:3 (1992), 263–304 | DOI | MR | Zbl

[14] Zheludev V. A., “Periodic splines and wavelets”, Mathematical Analysis, Wavelets, and Signal Processing (Cairo, 1994), Contemp. Math., 190, Amer. Math. Soc., Providence, RI, 1995, 339–354 | MR | Zbl

[15] Petukhov A. P., “Periodicheskie vspleski”, Mat. sb., 188:10 (1997), 69–94 | MR | Zbl

[16] Goh S. S., Lee S. L., Shen Z., Tang W. S., “Construction of Schauder decomposition on Banach spaces of periodic functions”, Proc. Edinburgh Math. Soc. (2), 41:1 (1998), 61–91 | DOI | MR | Zbl

[17] Sadovnichii V. A., Teoriya operatorov, Vyssh. shk., M., 1999

[18] Wojtaszczyk P., A mathematical introduction to wavelets, London Math. Soc. Stud. Texts, 37, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[19] Skopina M., “Multiresolution analysis of periodic functions”, East J. Approx., 3:2 (1997), 203–224 | MR | Zbl

[20] Kelly S. E., Kon M. A., Raphael L. A., Local convergence for wavelet expansions, Preprint | MR

[21] Maksimenko I. E., Biortogonalnost masshtabiruyuschikh funktsii mnogikh peremennykh. Sovremennye problemy teorii approksimatsii, 2002 (to appear)

[22] Maksimenko I. E., “Dostatochnye usloviya biortogonalnosti masshtabiruyuschikh funktsii mnogikh peremennykh”, Optimization of Finite Element Approximations, Splines and Wavelets, 2nd Intemat. Conf. OFEA'2001. Vol. 2 (St. Petersburg, Russia, 2001), S.-Peterburg Univ., St. Petersburg, 2002, 80–91

[23] Zigmund A., Trigonometricheskie ryady, T. 2, Mir, M., 1965 | MR

[24] Petukhov A., “Trigonometric rational wavelet bases”, Self-Similar Systems, Internat. Workshop (July 30–August 7, 1998, Dubna, Russia), JINR, Dubna, 1999, 116–119 ; E5-99-38, JINR | MR

[25] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl