On regularization in superreflexive Banach spaces by infimal convolution formulas
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-H¨older derivatives (for some 0 < α ≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of v...
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 1998 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/43525 |
| Acceso en línea: | http://hdl.handle.net/11441/43525 |
| Access Level: | acceso abierto |
| Palabra clave: | Regularization in Banach spaces Convex functions |
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On regularization in superreflexive Banach spaces by infimal convolution formulasCepedello Boiso, ManuelRegularization in Banach spacesConvex functionsWe present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-H¨older derivatives (for some 0 < α ≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of ∆-convex C1,α functions converging uniformly on bounded sets to f and preserving the infimum and the set of minimizers of f. The techniques we develop are based on the use of extended inf-convolution formulas and convexity properties such as the preservation of smoothness for the convex envelope of certain differentiable functions.Ministerio de Educación y CienciaPolish Academy of Sciences, Institute of MathematicsAnálisis MatemáticoFQM260: Variable Compleja y Teoria de OperadoresMinisterio de Educación y Ciencia (MEC). España1998info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/43525reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésStudia Mathematica, 129 (3), 265-284.info:eu-repo/semantics/openAccessoai:idus.us.es:11441/435252026-06-17T12:51:07Z |
| dc.title.none.fl_str_mv |
On regularization in superreflexive Banach spaces by infimal convolution formulas |
| title |
On regularization in superreflexive Banach spaces by infimal convolution formulas |
| spellingShingle |
On regularization in superreflexive Banach spaces by infimal convolution formulas Cepedello Boiso, Manuel Regularization in Banach spaces Convex functions |
| title_short |
On regularization in superreflexive Banach spaces by infimal convolution formulas |
| title_full |
On regularization in superreflexive Banach spaces by infimal convolution formulas |
| title_fullStr |
On regularization in superreflexive Banach spaces by infimal convolution formulas |
| title_full_unstemmed |
On regularization in superreflexive Banach spaces by infimal convolution formulas |
| title_sort |
On regularization in superreflexive Banach spaces by infimal convolution formulas |
| dc.creator.none.fl_str_mv |
Cepedello Boiso, Manuel |
| author |
Cepedello Boiso, Manuel |
| author_facet |
Cepedello Boiso, Manuel |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Análisis Matemático FQM260: Variable Compleja y Teoria de Operadores Ministerio de Educación y Ciencia (MEC). España |
| dc.subject.none.fl_str_mv |
Regularization in Banach spaces Convex functions |
| topic |
Regularization in Banach spaces Convex functions |
| description |
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-H¨older derivatives (for some 0 < α ≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of ∆-convex C1,α functions converging uniformly on bounded sets to f and preserving the infimum and the set of minimizers of f. The techniques we develop are based on the use of extended inf-convolution formulas and convexity properties such as the preservation of smoothness for the convex envelope of certain differentiable functions. |
| publishDate |
1998 |
| dc.date.none.fl_str_mv |
1998 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion |
| format |
article |
| status_str |
submittedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11441/43525 |
| url |
http://hdl.handle.net/11441/43525 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Studia Mathematica, 129 (3), 265-284. |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Polish Academy of Sciences, Institute of Mathematics |
| publisher.none.fl_str_mv |
Polish Academy of Sciences, Institute of Mathematics |
| dc.source.none.fl_str_mv |
reponame:idUS. Depósito de Investigación de la Universidad de Sevilla instname:Universidad de Sevilla (US) |
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Universidad de Sevilla (US) |
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idUS. Depósito de Investigación de la Universidad de Sevilla |
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idUS. Depósito de Investigación de la Universidad de Sevilla |
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1869421947728691200 |
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15.301603 |