Infinite dimensional generalized Jacobian: Properties and calculus rules |
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Authors: | Zsolt Pá les |
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Affiliation: | a Institute of Mathematics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary b Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA |
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Abstract: | The extension to infinite dimensional domains of Clarke's generalized Jacobian is the focus of this paper. First, a generalization of a Fabian-Preiss theorem to the infinite dimensional setting is obtained. As a consequence, a new formula relating the Clarke's generalized Jacobians corresponding to finite dimensional spaces K, L with K⊆L is established. Furthermore, in the infinite dimensional case, basic properties pertaining the generalized Jacobian are developed and then an identification of this set-valued map is produced. Applications of these results in the form of chain rules including sum and product rules, and a computational formula for continuous selections are derived. |
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Keywords: | Generalized Jacobian Characterization of the generalized Jacobian Chain rule Sum rule Formula for a continuous selection |
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