Geodesic
Wavelets on general lattices, associated with general expanding maps of 𝐑ⁿ
Calogero, A.1
1Dipartimento di Matematica, Universitá di Milano, via Saldini 50, 20133 Milano, Italy
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 1-10

Voir la notice de l'article provenant de la source American Mathematical Society

DOI

In the context of a general lattice $\Gamma$ in $\mathbf {R}^n$ and a strictly expanding map $M$ which preserves the lattice, we characterize all the wavelet families, all the MSF wavelets, all the multiwavelets associated with a Multiresolution Analysis (MRA) of multiplicity $d\ge 1,$ and all the scaling functions. Moreover, we give several examples: in particular, we construct a single, MRA and $C^\infty (\mathbf {R}^n)$ wavelet, which is nonseparable and with compactly supported Fourier transform.
DOI : 10.1090/S1079-6762-99-00054-2

Calogero, A.  1

1 Dipartimento di Matematica, Universitá di Milano, via Saldini 50, 20133 Milano, Italy 
Calogero, A. Wavelets on general lattices, associated with general expanding maps of 𝐑ⁿ. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 1-10. doi: 10.1090/S1079-6762-99-00054-2
@article{10_1090_S1079_6762_99_00054_2,
     author = {Calogero, A.},
     title = {Wavelets on general lattices, associated with general expanding maps of {\ensuremath{\mathbf{R}}ⁿ}},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {1--10},
     year = {1999},
     volume = {05},
     doi = {10.1090/S1079-6762-99-00054-2},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00054-2/}
}
TY  - JOUR
AU  - Calogero, A.
TI  - Wavelets on general lattices, associated with general expanding maps of 𝐑ⁿ
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1999
SP  - 1
EP  - 10
VL  - 05
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00054-2/
DO  - 10.1090/S1079-6762-99-00054-2
ID  - 10_1090_S1079_6762_99_00054_2
ER  - 
%0 Journal Article
%A Calogero, A.
%T Wavelets on general lattices, associated with general expanding maps of 𝐑ⁿ
%J Electronic research announcements of the American Mathematical Society
%D 1999
%P 1-10
%V 05
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00054-2/
%R 10.1090/S1079-6762-99-00054-2
%F 10_1090_S1079_6762_99_00054_2

[1] Cohen, A. Ondelettes et traitement numérique du signal 1992

[2] Cohen, Albert, Daubechies, Ingrid Nonseparable bidimensional wavelet bases Rev. Mat. Iberoamericana 1993 51 137

[3] Dai, Xingde, Larson, David R., Speegle, Darrin M. Wavelet sets in 𝐑ⁿ J. Fourier Anal. Appl. 1997 451 456

[4] De Michele, L., Soardi, P. M. On multiresolution analysis of multiplicity 𝑑 Monatsh. Math. 1997 255 272

[5] Gripenberg, Gustaf A necessary and sufficient condition for the existence of a father wavelet Studia Math. 1995 207 226

[6] Geronimo, Jeffrey S., Hardin, Douglas P., Massopust, Peter R. Fractal functions and wavelet expansions based on several scaling functions J. Approx. Theory 1994 373 401

[7] Gröchenig, K., Madych, W. R. Multiresolution analysis, Haar bases, and self-similar tilings of 𝑅ⁿ IEEE Trans. Inform. Theory 1992 556 568

[8] Hervé, Loïc Multi-resolution analysis of multiplicity 𝑑: applications to dyadic interpolation Appl. Comput. Harmon. Anal. 1994 299 315

[9] Hernández, Eugenio, Weiss, Guido A first course on wavelets 1996

[10] Hernández, Eugenio, Wang, Xihua, Weiss, Guido Smoothing minimally supported frequency wavelets. I J. Fourier Anal. Appl. 1996 329 340

[11] Hernández, Eugenio, Wang, Xihua, Weiss, Guido Smoothing minimally supported frequency wavelets. II J. Fourier Anal. Appl. 1997 23 41

[12] Les ondelettes en 1989 1990

[13] Madych, Wally R. Some elementary properties of multiresolution analyses of 𝐿²(𝑅ⁿ) 1992 259 294

[14] Meyer, Yves Ondelettes et opérateurs. I 1990

[15] Strang, Gilbert, Nguyen, Truong Wavelets and filter banks 1996

[16] Strichartz, Robert S. Construction of orthonormal wavelets 1994 23 50

[17] Strichartz, Robert S. Wavelets and self-affine tilings Constr. Approx. 1993 327 346

Cité par Sources :