Linear Functional Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Springer London
2000
|
| Schriftenreihe: | Springer Undergraduate Mathematics Series
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. Further highlights of the second edition include: a new chapter on the Hahn–Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; plenty of exercises, with solutions provided at the back of the book. Praise for the first edition: "The authors write with a strong narrative thrust and a sensitive appreciation of the needs of the average student so that, by the final chapter, there is a real feeling of having 'gotten somewhere worth getting' by a sensibly paced, clearly signposted route." Mathematical Gazette "It is a fine book, with material well-organized and well-presented. A particularly useful feature is the material on compact operators and applications to differential equations." CHOICE |
| Beschreibung: | 1 Online-Ressource (X, 273 p) |
| ISBN: | 9781447136552 9781852332570 |
| ISSN: | 1615-2085 |
| DOI: | 10.1007/978-1-4471-3655-2 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4471-3655-2 |
| format | Electronic eBook |
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| id | DE-604.BV042419379 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781447136552 9781852332570 |
| issn | 1615-2085 |
| language | English |
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| spelling | Rynne, Bryan Patrick Verfasser aut Linear Functional Analysis by Bryan Patrick Rynne, Martin Alexander Youngson London Springer London 2000 1 Online-Ressource (X, 273 p) txt rdacontent c rdamedia cr rdacarrier Springer Undergraduate Mathematics Series 1615-2085 This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. Further highlights of the second edition include: a new chapter on the Hahn–Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; plenty of exercises, with solutions provided at the back of the book. Praise for the first edition: "The authors write with a strong narrative thrust and a sensitive appreciation of the needs of the average student so that, by the final chapter, there is a real feeling of having 'gotten somewhere worth getting' by a sensibly paced, clearly signposted route." Mathematical Gazette "It is a fine book, with material well-organized and well-presented. A particularly useful feature is the material on compact operators and applications to differential equations." CHOICE Mathematics Global analysis (Mathematics) Analysis Mathematik Lineare Funktionalanalysis (DE-588)4114425-9 gnd rswk-swf Lineare Funktionalanalysis (DE-588)4114425-9 s 1\p DE-604 Youngson, Martin Alexander Sonstige oth https://doi.org/10.1007/978-1-4471-3655-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rynne, Bryan Patrick Linear Functional Analysis Mathematics Global analysis (Mathematics) Analysis Mathematik Lineare Funktionalanalysis (DE-588)4114425-9 gnd |
| subject_GND | (DE-588)4114425-9 |
| title | Linear Functional Analysis |
| title_auth | Linear Functional Analysis |
| title_exact_search | Linear Functional Analysis |
| title_full | Linear Functional Analysis by Bryan Patrick Rynne, Martin Alexander Youngson |
| title_fullStr | Linear Functional Analysis by Bryan Patrick Rynne, Martin Alexander Youngson |
| title_full_unstemmed | Linear Functional Analysis by Bryan Patrick Rynne, Martin Alexander Youngson |
| title_short | Linear Functional Analysis |
| title_sort | linear functional analysis |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Lineare Funktionalanalysis (DE-588)4114425-9 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Lineare Funktionalanalysis |
| url | https://doi.org/10.1007/978-1-4471-3655-2 |
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