Navegar

Colección

Datos Estadísticas

Artículo

Cabrelli, C.A.; Gordillo, M.L. "Existence of multiwavelets in ℝn" (2002) Proceedings of the American Mathematical Society. 130(5):1413-1424
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

For a q-regular Multiresolution Analysis of multiplicity r with arbitrary dilation matrix A for a general lattice Γ in ℝn, we give necessary and sufficient conditions in terms of the mask and the symbol of the vector scaling function in order that an associated wavelet basis exists. We also show that if 2r(m - 1) ≥ n where m is the absolute value of the determinant of A, then these conditions are always met, and therefore an associated wavelet basis of q-regular functions always exists. This extends known results to the case of multiwavelets in several variables with an arbitrary dilation matrix A for a lattice Γ.

Registro:

Documento: Artículo
Título:Existence of multiwavelets in ℝn
Autor:Cabrelli, C.A.; Gordillo, M.L.
Filiación:Departamento de Matemátic, Ciudad Universitaria, Universidad de buenos aires, Pabellón i, 1428 Capital Federal, Argentina
Palabras clave:Dilation matrix; Multiresolution Analysis; Multiwavelets; Non-separable wavelets; Wavelets
Año:2002
Volumen:130
Número:5
Página de inicio:1413
Página de fin:1424
DOI: http://dx.doi.org/10.1090/S0002-9939-01-06223-2
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v130_n5_p1413_Cabrelli

Referencias:

  • Aldroubi, A., Oblique and hierarchical multiwavelet bases (1997) Appl. Comput. Harmon. Anal., 4 (3), pp. 231-263. , [Ald97] MR 98k:42037
  • Alpert, B., A class of bases in L2 for the sparse representation of integral operators (1993) SIAM J. Math. Anal., 24 (1), pp. 246-262. , [Alp93] MR 93k:65104
  • Ashino, R., Kametani, M., A lemma on matrices and a construction of multiwavelets (1997) Math. Japan, 45, pp. 267-287. , [AK97] MR 98c:42025
  • Cabrelli, C., Heil, C., Molter, U., (1999) Self-Similarity and Multiwavelets in Higher Dimensions, , [CHM99] preprint
  • Calogero, A., Wavelets on general lattices associated with general expanding maps of Rn (1999) Electron. Res. Announc. Amer. Math. Soc., 5, pp. 1-10. , [Cal99] (electronic). MR 99i:42042
  • Chen, D.-R., On the existence and construction of orthonormal wavelets on L2(ℝs) (1997) Proc. Amer. Math. Soc., 125, pp. 2883-2889. , [Che97] MR 98h:42030
  • Cohen, A., Daubechies, I., Plonka, G., Regularity of refinable function vectors (1997) J. Fourier Anal. Appl., 3 (3), pp. 295-324. , [CDP97] MR 98e:42031
  • Daubechies, I., Orthonormal bases of compactly supported wavelets (1988) Comm. Pure and Appl. Math., 41, pp. 909-996. , [Dau88] MR 90m:42039
  • De Michele, L., Soardi, P.-M., On multiresolution analysis of multiplicity d (1997) Mh. Math., 124, pp. 255-272. , [DS97] MR 98k:42039
  • Geronimo, J., Hardin, D., Massopust, P., Fractal functions and wavelet expansions based on several scaling functions (1994) J. Approx. Theory, 78 (3), pp. 373-401. , [GHM94] MR 95h:42033
  • Goodman, T.N.T., Lee, S.L., Tang, W.S., Wavelets in wandering subspaces (1993) Trans. Amer. Math. Soc., 338 (2), pp. 639-654. , [GLT93] MR 93j:42017
  • Gröchenig, K., Analyse multiéchelles et bases d'ondelettes (1987) C. R. Acad. Sci. Paris Sér. I Math., 305, pp. 13-15. , [Gro87] MR 88j:47036
  • Gröchenig, K., Madych, W., Multiresolution analysis, Haar bases and self-similar tilings (1992) IEEE Trans. Inform. Theory, 38, pp. 556-568. , [GM92] MR 93i:42001
  • Heil, C., Colella, D., Matrix refinement equations: Existence and uniqueness (1996) J. Fourier Anal. Appl., 2 (4), pp. 363-377. , [HC96] MR 97k:39021
  • Heil, C., Strang, G., Strela, V., Approximation by translates of refinable functions (1996) Numer. Math., 73 (1), pp. 75-94. , [HSS96] MR 97c:65033
  • Hutchinson, J., Fractals and Self-similarity (1981) Indiana Univ. Math. J., 3, pp. 713-747. , [Hut81] MR 82h:49026
  • Jia, R.-Q., Riemenschneider, S., Zhou, D.-X., Smoothness of multiple refinable functions and multiple wavelets (1999) SIAM J. Matrix Anal. Appl., 21 (1), pp. 1-28. , [JRZ99] (electronic). MR 2000k:42050
  • Mallat, S., Multiresolution approximations and wavelet orthonormal basis of L2(R) (1989) Trans. Amer. Math. Soc., 315, pp. 69-87. , [Ma189] MR 90e:42046
  • Meyer, Y., (1992) Wavelets and Operators, , [Mey92] Cambridge University Press, Cambridge, MR 94f:42001
  • Potiopa, A., (1997) A problem of Lagarias and Wang, , [Pot97] Master's thesis, Siedlce University, Siedlce, Poland June, Polish
  • Wojtaszczyk, P., (1997) A Mathematical Introduction to Wavelets, , [Woj97] Cambridge University Press, MR 98j:42025

Citas:

---------- APA ----------
Cabrelli, C.A. & Gordillo, M.L. (2002) . Existence of multiwavelets in ℝn. Proceedings of the American Mathematical Society, 130(5), 1413-1424.
http://dx.doi.org/10.1090/S0002-9939-01-06223-2
---------- CHICAGO ----------
Cabrelli, C.A., Gordillo, M.L. "Existence of multiwavelets in ℝn" . Proceedings of the American Mathematical Society 130, no. 5 (2002) : 1413-1424.
http://dx.doi.org/10.1090/S0002-9939-01-06223-2
---------- MLA ----------
Cabrelli, C.A., Gordillo, M.L. "Existence of multiwavelets in ℝn" . Proceedings of the American Mathematical Society, vol. 130, no. 5, 2002, pp. 1413-1424.
http://dx.doi.org/10.1090/S0002-9939-01-06223-2
---------- VANCOUVER ----------
Cabrelli, C.A., Gordillo, M.L. Existence of multiwavelets in ℝn. Proc. Am. Math. Soc. 2002;130(5):1413-1424.
http://dx.doi.org/10.1090/S0002-9939-01-06223-2