Generalized Self-Similarity

Autores
Cabrelli, C.A.; Molter, U.M.
Año de publicación
1999
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fuente
J. Math. Anal. Appl. 1999;230(1):251-260
Materia
Dilation equation
Fixed points
Fractals
Functional equation
Inverse problem for fractals
Refinement equation
Self-similarity
Wavelets
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0022247X_v230_n1_p251_Cabrelli
Acceder
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oai_identifier_str paperaa:paper_0022247X_v230_n1_p251_Cabrelli
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Generalized Self-SimilarityCabrelli, C.A.Molter, U.M.Dilation equationFixed pointsFractalsFunctional equationInverse problem for fractalsRefinement equationSelf-similarityWaveletsWe 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.1999info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0022247X_v230_n1_p251_CabrelliJ. Math. Anal. Appl. 1999;230(1):251-260reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:43:09Zpaperaa:paper_0022247X_v230_n1_p251_CabrelliInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:43:10.248Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Generalized Self-Similarity
title Generalized Self-Similarity
spellingShingle Generalized Self-Similarity
Cabrelli, C.A.
Dilation equation
Fixed points
Fractals
Functional equation
Inverse problem for fractals
Refinement equation
Self-similarity
Wavelets
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
dc.creator.none.fl_str_mv Cabrelli, C.A.
Molter, U.M.
author Cabrelli, C.A.
author_facet Cabrelli, C.A.
Molter, U.M.
author_role author
author2 Molter, U.M.
author2_role author
dc.subject.none.fl_str_mv Dilation equation
Fixed points
Fractals
Functional equation
Inverse problem for fractals
Refinement equation
Self-similarity
Wavelets
topic Dilation equation
Fixed points
Fractals
Functional equation
Inverse problem for fractals
Refinement equation
Self-similarity
Wavelets
dc.description.none.fl_txt_mv 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.
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.
publishDate 1999
dc.date.none.fl_str_mv 1999
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_0022247X_v230_n1_p251_Cabrelli
url http://hdl.handle.net/20.500.12110/paper_0022247X_v230_n1_p251_Cabrelli
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Math. Anal. Appl. 1999;230(1):251-260
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 13.070432

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