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
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v230_n1_p251_Cabrelli_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_0022247X_v230_n1_p251_Cabrelli_oai
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spelling	I28-R145-paper_0022247X_v230_n1_p251_Cabrelli_oai2024-08-16 Cabrelli, C.A. Molter, U.M. 1999 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. application/pdf http://hdl.handle.net/20.500.12110/paper_0022247X_v230_n1_p251_Cabrelli info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Anal. Appl. 1999;230(1):251-260 Dilation equation Fixed points Fractals Functional equation Inverse problem for fractals Refinement equation Self-similarity Wavelets Generalized Self-Similarity info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v230_n1_p251_Cabrelli_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v230_n1_p251_Cabrelli_oai
work_keys_str_mv	AT cabrellica generalizedselfsimilarity AT molterum generalizedselfsimilarity
_version_	1809357200605315072

Generalized Self-Similarity

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