Density of the set of generators of wavelet systems

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Given a function ψ in L2(Rd), the affine (wavelet) system generated by ψ, associated to an invertible matrix a and a lattice Γ, is the collection of functions {|det a|j/2ψ (ajx - γ) : j ∈ Z, γ ∈ Γ}. In this paper we prove that the set of functions generating affine systems that are a Riesz basis of...

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Autor principal: Cabrelli, C.
Otros Autores: Molter, U.M
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2007
Acceso en línea:Registro en Scopus
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100 1 |a Cabrelli, C. 
245 1 0 |a Density of the set of generators of wavelet systems 
260 |c 2007 
270 1 0 |m Cabrelli, C.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Capital Federal, Argentina; email: cabrelli@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a ALDROUBI, A., CABRELLI, C.A., MOLTER, U., Wavelets on irregular grids with arbitrary dilation matrices, and frame atoms for L2(Rd ) (2004) Appl. Comput. Harmon. Anal, 17 (2), pp. 171-191. , ACM04 
504 |a [Beu66] A. BEURLING (1966): Local harmonic analysis with some applications to differential operators. Some Recent Advances in the Basic Sciences, 1 (Proc. Annual Sci. Conf., Belfer Grad. School Sci., Yeshiva University, New York, 1962-1964), Belfer Graduate School of Science, Yeshiva University, New York, pp. 109-125; BENEDETTO, J.J., FRAZIER, M.W., (1994) Introduction, Wavelets: Mathematics and Applications. Studies in Advanced Mathematics, pp. 1-20. , BF94, Boca Raton, FL: CRC, pp 
504 |a BENEDETTO, J.J., LEON, M., The construction of single wavelets in d-dimensions (2001) J. Geom. Anal, 11 (1), pp. 1-15. , BL01 
504 |a BAGGETT, L.W., MEDINA, H.A., MERRILL, K.D., Generalized multi-resolution analyses and a construction procedure for all wavelet sets in Rn (1999) J. Fourier Anal. Appl, 5 (6), pp. 563-573. , BMM99 
504 |a BOWNIK, M., Quasi-affine systems and the Calderón condition (2001) Contemporary Mathematics, 320, pp. 29-43. , Bow03, Harmonic Analysis at Mount Holyoke South Hadley, MA, Providence, RI: Amer. Math. Soc, pp 
504 |a BOWNIK, M., (2005) Connectivity and density in the set of framelets, , Bow05, Preprint 
504 |a BENEDETTO, J.J., SUMETKIJAKAN, S., A fractal set constructed from a class of wavelet sets (2001) Contemporary Mathematics, 313, pp. 19-35. , BS02, Inverse Problems, Image Analysis, and Medical Imaging New Orleans, LA, Providence, RI: Amer. Math. Soc, pp 
504 |a BENEDETTO, J.J., SUMETKIJAKAN, S., (2004) Tight frames and geometric properties of wavelet sets, , BS04, Preprint 
504 |a BENEDETTO, J.J., WU, H.C., Non-uniform sampling and spiral MRI reconstruction (1999) Proc. SampTA, 99. , BW99, Trondheim, Norway 
504 |a CHUI, C.K., CZAJA, W., MAGGIONI, M., WEISS, G., Characterization of general tight wavelet frames with matrix dilations and tightness preserving oversampling (2002) J. Fourier Anal. Appl, 8 (2), pp. 173-200. , CCMW02 
504 |a CABRELLI, C., HEIL, C., MOLTER, U., Self-similarity and multiwavelets in higher dimensions (2004) Mem. Amer. Math. Soc, 170. , CHM04 
504 |a Basic properties of wavelets (1998) J. Fourier Anal. Appl, 4 (4-5), pp. 575-594. , Con98] The Wutam Consortium 
504 |a CHUI, C.K., SHI, X., Orthonormal wavelets and tight frames with arbitrary real dilations (2000) Appl. Comput. Harmon. Anal, 9 (3), pp. 243-264. , CS00 
504 |a DAUBECHIES, I., Orthonormal bases of compactly supported wavelets (1988) Comm. Pure Appl. Math, 41, pp. 909-996. , Dau88 
504 |a DAI, X., LARSON, D.R., (1998) Wandering vectors for unitary systems and orthogonal wavelets, 134. , DL98, Mem. Amer. Math. Soc, 640:viii+68 
504 |a DAI, X., LARSON, D.R., SPEEGLE, D.M., Wavelet sets in Rn (1997) J. Fourier Anal. Appl, 3 (4), pp. 451-456. , DLS97, MR 98m:42048 
504 |a DAI, X., LARSON, D.R., SPEEGLE, D.M., Wavelet sets in Rn, II (1997) Wavelets, Multiwavelets, and Their Applications, pp. 15-40. , DLS98, San Diego, CA, Providence, RI: Amer. Math. Soc, pp, MR 99d:42054 
504 |a [GLL+04] K. GUO, D. LABATE, W.-Q LIM, G. WEISS, E. WILSON (2004): Wavelets with composite dilations. Electron. Res. Announc. Amer. Math. Soc., 10:78-87 (electronic); GOODMAN, T.N.T., LEE, S.L., TANG, W.-S., Wavelets in wandering subspaces (1993) Trans. Amer. Math. Soc, 338, pp. 639-654. , GLT93 
504 |a IONASCU, E.J., LARSON, D.R., PEARCY, C.M., On wavelet sets (1998) J. Fourier Anal. Appl, 4 (6), pp. 711-721. , ILP98 
504 |a JIMENEZ, D., WANG, L., WANG, Y., (2005) PCM quantization errors and the white noise hypothesis, , JWW05, Preprint 
504 |a LARSON, D., Unitary systems and wavelet sets (2005) Proceedings of the Fourth ICWAA, pp. 5-35. , Lar05, Macau: Springer, pp 
504 |a MALLAT, S., Multiresolution approximations and wavelet orthonormal basis of L2(R) (1989) Trans. Amer. Math. Soc, 315 (1), pp. 69-87. , Mal89 
504 |a MEYER, Y., (1988) Ondelettes et operateurs, 1. , Mey88, Paris: Hermann 
504 |a MEYER, Y., (1992) Wavelets and Operators, , Mey92, Cambridge: Cambridge University Press 
504 |a SPEEGLE, D.M., The s-elementary wavelets are path-connected (1999) Proc. Amer. Math. Soc, 127 (1), pp. 223-233. , Spe99 
504 |a SOARDI, P.M., WEILAND, D., Single wavelets in n-dimensions (1998) J. Fourier Anal. Appl, 4 (3), pp. 299-315. , SW98 
504 |a WANG, Y., Wavelets, tiling, and spectral sets (2002) Duke Math. J, 114 (1), pp. 43-57. , Wan02 
504 |a ZAKHAROV, V., (1996) Nonseparable multidimensional Littlewood-Paley-like wavelet bases, , Zak96, Preprint 
520 3 |a Given a function ψ in L2(Rd), the affine (wavelet) system generated by ψ, associated to an invertible matrix a and a lattice Γ, is the collection of functions {|det a|j/2ψ (ajx - γ) : j ∈ Z, γ ∈ Γ}. In this paper we prove that the set of functions generating affine systems that are a Riesz basis of L2(Rd) is dense in L2(Rd). We also prove that a stronger result is true for affine systems that are a frame of L2(Rd). In this case we show that the generators associated to a fixed but arbitrary dilation are a dense set. Furthermore, we analyze the orthogonal case in which we prove that the set of generators of orthogonal (not necessarily complete) affine systems, that are compactly supported in frequency, are dense in the unit sphere of L2(R d) with the induced metric. As a byproduct we introduce the p-Grammian of a function and prove a convergence result of this Grammian as a function of the lattice. This result gives insight in the problem of oversampling of affine systems. © 2007 Springer.  |l eng 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Capital Federal, Argentina 
593 |a CONICET, Argentina 
690 1 0 |a AFFINE SYSTEMS 
690 1 0 |a RIESZ BASIS WAVELETS 
690 1 0 |a WAVELET FRAMES 
690 1 0 |a WAVELET SET 
700 1 |a Molter, U.M. 
773 0 |d 2007  |g v. 26  |h pp. 65-81  |k n. 1  |p Constr. Approx.  |x 01764276  |t Constructive Approximation 
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