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rdf:type
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Description
| - Let X be a separable superreflexive Banach space and f be a semiconvex function (with a general modulus) on X. For k epsilon N, let Sigma(k)(f) be the set of points x epsilon X, at which the Clarke subdifferential partial derivative f(x) is at least k-dimensional. Note that Sigma(1)(f) is the set of all points at which f is not Gateaux differentiable. Then Sigma(k)(f) can be covered by countably many Lipschitz surfaces of codimension k which are described by functions, which are differences of two semiconvex functions. If X is separable and superreflexive Banach space which admits an equivalent norm with modulus of smoothness of power type 2 (e.g., if X is a Hilbert space or X = L-p(mu) with 2 {= p), we give, for a fixed modulus w and k epsilon N, a complete characterization of those A subset of X, for which there exists a function f on X which is semiconvex on X with modulus w and A subset of Sigma(k)(f). Namely, A subset of X has this property if and only if A can be covered by countably many Lipschitz surfaces S-n f codimension k which are described by functions, which are differences of two Lipschitz semiconvex functions with modulus C(n)w.
- Let X be a separable superreflexive Banach space and f be a semiconvex function (with a general modulus) on X. For k epsilon N, let Sigma(k)(f) be the set of points x epsilon X, at which the Clarke subdifferential partial derivative f(x) is at least k-dimensional. Note that Sigma(1)(f) is the set of all points at which f is not Gateaux differentiable. Then Sigma(k)(f) can be covered by countably many Lipschitz surfaces of codimension k which are described by functions, which are differences of two semiconvex functions. If X is separable and superreflexive Banach space which admits an equivalent norm with modulus of smoothness of power type 2 (e.g., if X is a Hilbert space or X = L-p(mu) with 2 {= p), we give, for a fixed modulus w and k epsilon N, a complete characterization of those A subset of X, for which there exists a function f on X which is semiconvex on X with modulus w and A subset of Sigma(k)(f). Namely, A subset of X has this property if and only if A can be covered by countably many Lipschitz surfaces S-n f codimension k which are described by functions, which are differences of two Lipschitz semiconvex functions with modulus C(n)w. (en)
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Title
| - Smallness of Singular Sets of Semiconvex Functions in Separable Banach Spaces
- Smallness of Singular Sets of Semiconvex Functions in Separable Banach Spaces (en)
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skos:prefLabel
| - Smallness of Singular Sets of Semiconvex Functions in Separable Banach Spaces
- Smallness of Singular Sets of Semiconvex Functions in Separable Banach Spaces (en)
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skos:notation
| - RIV/00216208:11320/13:10189657!RIV14-GA0-11320___
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/09/0067), Z(MSM0021620839)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/13:10189657
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - superreflexive space; DSC surface; Lipschitz surface; singular point of order k; singular set; Clarke subdifferential; Semiconvex function with general modulus (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - DE - Spolková republika Německo
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Journal of Convex Analysis
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Duda, Jakub
- Zajíček, Luděk
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http://linked.open...ain/vavai/riv/wos
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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