Search results for "Composite function"

showing 3 items of 3 documents

A note on Fréchet and approximate subdifferentials of composite functions

1994

The aim of this note is to present in the reflexive Banach space setting a natural and simple proof of the formula of the approximate subdifferential of a composite function.

Composite functionMathematics::Functional AnalysisPure mathematicsSimple (abstract algebra)General MathematicsComposite numberBanach spaceSubderivativeMathematicsBulletin of the Australian Mathematical Society
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Metric regularity and subdifferential calculus in Banach spaces

1995

In this paper we give verifiable conditions in terms of limiting Frechet subdifferentials ensuring the metric regularity of a multivalued functionF(x)=−g(x)+D. We apply our results to the study of the limiting Frechet subdifferential of a composite function defined on a Banach space.

Discrete mathematicsComposite functionPure mathematicsApplied MathematicsBanach spaceLimitingSubderivativemedicine.diseaseMetric (mathematics)medicineVerifiable secret sharingAnalysisCalculus (medicine)MathematicsSet-Valued Analysis
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Composition operators on the Schwartz space

2018

[EN] We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition operator to be closed. These conditions are expressed in terms of multipliers for the Schwartz class and the closed range property of the corresponding operator considered in the space of smooth functions.

Space of rapidly decreasing functionsPure mathematicsClass (set theory)Composition operatorGeneral MathematicsComposite function problem010102 general mathematicsComposition (combinatorics)Space (mathematics)Compact operator01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsRange (mathematics)47B33 46F05 47A05Operator (computer programming)Schwartz spaceFOS: MathematicsComposition operator0101 mathematicsMATEMATICA APLICADAMathematicsRevista Matemática Iberoamericana
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