Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2012]
|
| Schriftenreihe: | Annals of Mathematics Studies
number179 |
| Schlagworte: | |
| Online-Zugang: | URL des Erstveröffentlichers Volltext |
| Beschreibung: | Biographical note: Joram Lindenstrauss is professor emeritus of mathematics at the Hebrew University of Jerusalem. David Preiss is professor of mathematics at the University of Warwick. Jaroslav Ti¿er is associate professor of mathematics at Czech Technical University in Prague Main description: This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics |
| Beschreibung: | 1 Online-Ressource (440 S.) |
| ISBN: | 9781400842698 |
Internformat
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| 500 | |a Biographical note: Joram Lindenstrauss is professor emeritus of mathematics at the Hebrew University of Jerusalem. David Preiss is professor of mathematics at the University of Warwick. Jaroslav Ti¿er is associate professor of mathematics at Czech Technical University in Prague | ||
| 500 | |a Main description: This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics | ||
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Datensatz im Suchindex
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| author | Lindenstrauss, Joram 1936-2012 Preiss, David 1947- Tišer, Jaroslav |
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| author_facet | Lindenstrauss, Joram 1936-2012 Preiss, David 1947- Tišer, Jaroslav |
| author_role | aut aut aut |
| author_sort | Lindenstrauss, Joram 1936-2012 |
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| building | Verbundindex |
| bvnumber | BV042523025 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.88 |
| dewey-search | 515.88 |
| dewey-sort | 3515.88 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV042523025 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-19T17:41:08Z |
| institution | BVB |
| isbn | 9781400842698 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027957364 |
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| publisher | Princeton University Press |
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| series | Annals of Mathematics Studies |
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| spelling | Lindenstrauss, Joram 1936-2012 (DE-588)172227127 aut Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces Princeton, N.J. Princeton University Press [2012] © 2012 1 Online-Ressource (440 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number179 Biographical note: Joram Lindenstrauss is professor emeritus of mathematics at the Hebrew University of Jerusalem. David Preiss is professor of mathematics at the University of Warwick. Jaroslav Ti¿er is associate professor of mathematics at Czech Technical University in Prague Main description: This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics Lipschitz-Bedingung (DE-588)4167811-4 gnd rswk-swf Fréchet-Differenzierbarkeit (DE-588)4370829-8 gnd rswk-swf Lipschitz-Bedingung (DE-588)4167811-4 s Fréchet-Differenzierbarkeit (DE-588)4370829-8 s 1\p DE-604 Preiss, David 1947- (DE-588)1042745919 aut Tišer, Jaroslav (DE-588)143333429 aut Erscheint auch als Druck-Ausgabe 978-0-691-15355-1 Annals of Mathematics Studies number179 (DE-604)BV040389493 179 http://www.degruyter.com/doi/book/10.1515/9781400842698?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400842698&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lindenstrauss, Joram 1936-2012 Preiss, David 1947- Tišer, Jaroslav Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces Annals of Mathematics Studies Lipschitz-Bedingung (DE-588)4167811-4 gnd Fréchet-Differenzierbarkeit (DE-588)4370829-8 gnd |
| subject_GND | (DE-588)4167811-4 (DE-588)4370829-8 |
| title | Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces |
| title_auth | Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces |
| title_exact_search | Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces |
| title_full | Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces |
| title_fullStr | Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces |
| title_full_unstemmed | Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces |
| title_short | Frechet differentiability of Lipschitz functions and Porous sets in Banach spaces |
| title_sort | frechet differentiability of lipschitz functions and porous sets in banach spaces |
| topic | Lipschitz-Bedingung (DE-588)4167811-4 gnd Fréchet-Differenzierbarkeit (DE-588)4370829-8 gnd |
| topic_facet | Lipschitz-Bedingung Fréchet-Differenzierbarkeit |
| url | http://www.degruyter.com/doi/book/10.1515/9781400842698?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400842698&searchTitles=true |
| volume_link | (DE-604)BV040389493 |
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