Generalized Self-Similarity

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We prove the existence of Lpfunctions satisfying a kind of self-similarity condition. This is achieved by solving a functional equation by means of the construction of a contractive operator on an appropriate functional space. The solution, a fixed point of the operator, can be obtained by an iterat...

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Autores principales: Cabrelli, C.A., Molter, U.M.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 1999
Materias:
Dilation equation
Fixed points
Fractals
Functional equation
Inverse problem for fractals
Refinement equation
Self-similarity
Wavelets
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v230_n1_p251_Cabrelli
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_0022247X_v230_n1_p251_Cabrelli
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spelling paperaa:paper_0022247X_v230_n1_p251_Cabrelli2023-06-12T16:44:02Z Generalized Self-Similarity J. Math. Anal. Appl. 1999;230(1):251-260 Cabrelli, C.A. Molter, U.M. Dilation equation Fixed points Fractals Functional equation Inverse problem for fractals Refinement equation Self-similarity Wavelets We prove the existence of Lpfunctions satisfying a kind of self-similarity condition. This is achieved by solving a functional equation by means of the construction of a contractive operator on an appropriate functional space. The solution, a fixed point of the operator, can be obtained by an iterative process, making this model very suitable to use in applications such as fractal image and signal compression. On the other hand, this "generalized self-similarity equation" includes matrix refinement equations of the typef(x)=∑ckf(Ax-k) which are central in the construction of wavelets and multiwavelets. The results of this paper will therefore yield conditions for the existence of Lp-refinable functions in a very general setting. © 1998 Academic Press. Fil:Cabrelli, C.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Molter, U.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1999 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v230_n1_p251_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Dilation equation
Fixed points
Fractals
Functional equation
Inverse problem for fractals
Refinement equation
Self-similarity
Wavelets
spellingShingle Dilation equation
Fixed points
Fractals
Functional equation
Inverse problem for fractals
Refinement equation
Self-similarity
Wavelets
Cabrelli, C.A.
Molter, U.M.
Generalized Self-Similarity
topic_facet Dilation equation
Fixed points
Fractals
Functional equation
Inverse problem for fractals
Refinement equation
Self-similarity
Wavelets
description We prove the existence of Lpfunctions satisfying a kind of self-similarity condition. This is achieved by solving a functional equation by means of the construction of a contractive operator on an appropriate functional space. The solution, a fixed point of the operator, can be obtained by an iterative process, making this model very suitable to use in applications such as fractal image and signal compression. On the other hand, this "generalized self-similarity equation" includes matrix refinement equations of the typef(x)=∑ckf(Ax-k) which are central in the construction of wavelets and multiwavelets. The results of this paper will therefore yield conditions for the existence of Lp-refinable functions in a very general setting. © 1998 Academic Press.
format Artículo
Artículo
publishedVersion
author Cabrelli, C.A.
Molter, U.M.
author_facet Cabrelli, C.A.
Molter, U.M.
author_sort Cabrelli, C.A.
title Generalized Self-Similarity
title_short Generalized Self-Similarity
title_full Generalized Self-Similarity
title_fullStr Generalized Self-Similarity
title_full_unstemmed Generalized Self-Similarity
title_sort generalized self-similarity
publishDate 1999
url http://hdl.handle.net/20.500.12110/paper_0022247X_v230_n1_p251_Cabrelli
work_keys_str_mv AT cabrellica generalizedselfsimilarity
AT molterum generalizedselfsimilarity
_version_ 1769810321801740288

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