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
Autores principales:	Cabrelli, C.A., Gordillo, M.L.
Formato:	JOUR
Materias:	Dilation matrix Multiresolution Analysis Multiwavelets Non-separable wavelets Wavelets
Acceso en línea:	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	todo:paper_00029939_v130_n5_p1413_Cabrelli
record_format	dspace
spelling	todo:paper_00029939_v130_n5_p1413_Cabrelli2023-10-03T13:55:06Z Existence of multiwavelets in ℝn Cabrelli, C.A. Gordillo, M.L. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Cabrelli, C.A. Gordillo, M.L. 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.
format	JOUR
author	Cabrelli, C.A. Gordillo, M.L.
author_facet	Cabrelli, C.A. Gordillo, M.L.
author_sort	Cabrelli, C.A.
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
url	http://hdl.handle.net/20.500.12110/paper_00029939_v130_n5_p1413_Cabrelli
work_keys_str_mv	AT cabrellica existenceofmultiwaveletsinrn AT gordilloml existenceofmultiwaveletsinrn
_version_	1807315379765116928

Existence of multiwavelets in ℝn

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