Differentiable Operators and Nonlinear Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1994
|
| Schriftenreihe: | Operator Theory Advances and Applications
66 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | We have considered writing the present book for a long time, since the lack of a sufficiently complete textbook about complex analysis in infinite dimensional spaces was apparent. There are, however, some separate topics on this subject covered in the mathematical literature. For instance, the elementary theory of holomorphic vectorfunctions.and mappings on Banach spaces is presented in the monographs of E. Hille and R. Phillips [1] and L. Schwartz [1], whereas some results on Banach algebras of holomorphic functions and holomorphic operator-functions are discussed in the books of W. Rudin [1] and T. Kato [1]. Apparently, the need to study holomorphic mappings in infinite dimensional spaces arose for the first time in connection with the development of nonlinear analysis. A systematic study of integral equations with an analytic nonlinear part was started at the end ofthe 19th and the beginning ofthe 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods. The most complete presentation of these methods comes from N. Nazarov. In the forties and fifties the interest in Liapunov's and Schmidt's analytic methods diminished temporarily due to the appearence of variational calculus methods (M. Golomb, A. Hammerstein and others) and also to the rapid development of the mapping degree theory (J. Leray, J. Schauder, G. Birkhoff, O. Kellog and others) |
| Beschreibung: | 1 Online-Ressource (X, 284 p) |
| ISBN: | 9783034885126 9783034896580 |
| DOI: | 10.1007/978-3-0348-8512-6 |
Internformat
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Khatskevich, Victor |
| author_GND | (DE-588)1079700099 |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8512-6 |
| format | Electronic eBook |
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| id | DE-604.BV042422146 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034885126 9783034896580 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857563 |
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| physical | 1 Online-Ressource (X, 284 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series | Operator Theory Advances and Applications |
| series2 | Operator Theory Advances and Applications |
| spelling | Khatskevich, Victor Verfasser aut Differentiable Operators and Nonlinear Equations by Victor Khatskevich, David Shoiykhet Basel Birkhäuser Basel 1994 1 Online-Ressource (X, 284 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory Advances and Applications 66 We have considered writing the present book for a long time, since the lack of a sufficiently complete textbook about complex analysis in infinite dimensional spaces was apparent. There are, however, some separate topics on this subject covered in the mathematical literature. For instance, the elementary theory of holomorphic vectorfunctions.and mappings on Banach spaces is presented in the monographs of E. Hille and R. Phillips [1] and L. Schwartz [1], whereas some results on Banach algebras of holomorphic functions and holomorphic operator-functions are discussed in the books of W. Rudin [1] and T. Kato [1]. Apparently, the need to study holomorphic mappings in infinite dimensional spaces arose for the first time in connection with the development of nonlinear analysis. A systematic study of integral equations with an analytic nonlinear part was started at the end ofthe 19th and the beginning ofthe 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods. The most complete presentation of these methods comes from N. Nazarov. In the forties and fifties the interest in Liapunov's and Schmidt's analytic methods diminished temporarily due to the appearence of variational calculus methods (M. Golomb, A. Hammerstein and others) and also to the rapid development of the mapping degree theory (J. Leray, J. Schauder, G. Birkhoff, O. Kellog and others) Mathematics Global analysis (Mathematics) Analysis Mathematik Banach-Raum (DE-588)4004402-6 gnd rswk-swf Holomorphe Abbildung (DE-588)4160471-4 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Differenzierbarkeit (DE-588)4149807-0 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Holomorphe Abbildung (DE-588)4160471-4 s Banach-Raum (DE-588)4004402-6 s 1\p DE-604 Linearer Operator (DE-588)4167721-3 s Differenzierbarkeit (DE-588)4149807-0 s 2\p DE-604 Nichtlineare Analysis (DE-588)4177490-5 s 3\p DE-604 Shoiykhet, David 1953- Sonstige (DE-588)1079700099 oth Operator Theory Advances and Applications 66 (DE-604)BV035421307 66 https://doi.org/10.1007/978-3-0348-8512-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Khatskevich, Victor Differentiable Operators and Nonlinear Equations Operator Theory Advances and Applications Mathematics Global analysis (Mathematics) Analysis Mathematik Banach-Raum (DE-588)4004402-6 gnd Holomorphe Abbildung (DE-588)4160471-4 gnd Linearer Operator (DE-588)4167721-3 gnd Differenzierbarkeit (DE-588)4149807-0 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4160471-4 (DE-588)4167721-3 (DE-588)4149807-0 (DE-588)4177490-5 |
| title | Differentiable Operators and Nonlinear Equations |
| title_auth | Differentiable Operators and Nonlinear Equations |
| title_exact_search | Differentiable Operators and Nonlinear Equations |
| title_full | Differentiable Operators and Nonlinear Equations by Victor Khatskevich, David Shoiykhet |
| title_fullStr | Differentiable Operators and Nonlinear Equations by Victor Khatskevich, David Shoiykhet |
| title_full_unstemmed | Differentiable Operators and Nonlinear Equations by Victor Khatskevich, David Shoiykhet |
| title_short | Differentiable Operators and Nonlinear Equations |
| title_sort | differentiable operators and nonlinear equations |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Banach-Raum (DE-588)4004402-6 gnd Holomorphe Abbildung (DE-588)4160471-4 gnd Linearer Operator (DE-588)4167721-3 gnd Differenzierbarkeit (DE-588)4149807-0 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Banach-Raum Holomorphe Abbildung Linearer Operator Differenzierbarkeit Nichtlineare Analysis |
| url | https://doi.org/10.1007/978-3-0348-8512-6 |
| volume_link | (DE-604)BV035421307 |
| work_keys_str_mv | AT khatskevichvictor differentiableoperatorsandnonlinearequations AT shoiykhetdavid differentiableoperatorsandnonlinearequations |