Existence of multiwavelets in ℝn

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 tha...

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Detalles Bibliográficos
Publicado: 2002
Materias:
Dilation matrix
Multiresolution Analysis
Multiwavelets
Non-separable wavelets
Wavelets
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v130_n5_p1413_Cabrelli
http://hdl.handle.net/20.500.12110/paper_00029939_v130_n5_p1413_Cabrelli
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029939_v130_n5_p1413_Cabrelli
record_format dspace
spelling paper:paper_00029939_v130_n5_p1413_Cabrelli2023-06-08T14:23:25Z Existence of multiwavelets in ℝn Dilation matrix Multiresolution Analysis Multiwavelets Non-separable wavelets Wavelets 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. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v130_n5_p1413_Cabrelli http://hdl.handle.net/20.500.12110/paper_00029939_v130_n5_p1413_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Dilation matrix
Multiresolution Analysis
Multiwavelets
Non-separable wavelets
Wavelets
spellingShingle Dilation matrix
Multiresolution Analysis
Multiwavelets
Non-separable wavelets
Wavelets
Existence of multiwavelets in ℝn
topic_facet Dilation matrix
Multiresolution Analysis
Multiwavelets
Non-separable wavelets
Wavelets
description 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.
title Existence of multiwavelets in ℝn
title_short Existence of multiwavelets in ℝn
title_full Existence of multiwavelets in ℝn
title_fullStr Existence of multiwavelets in ℝn
title_full_unstemmed Existence of multiwavelets in ℝn
title_sort existence of multiwavelets in ℝn
publishDate 2002
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v130_n5_p1413_Cabrelli
http://hdl.handle.net/20.500.12110/paper_00029939_v130_n5_p1413_Cabrelli
_version_ 1768542482207866880

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