Applications of functional analysis and operator theory
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| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2005
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Mathematics in science and engineering
200 |
| Schlagworte: | |
| Online-Zugang: | Beschreibung für Leser Inhaltsverzeichnis Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1819751059130679296 |
|---|---|
| adam_text | APPLICATIONS OF FUNCTIONAL ANALYSIS AND OPERATOR THEORY SECOND EDITION
VIVIAN HUTSON UNIVERSITY OF SHEFFIELD SHEFFIELD, UK JOHN S. PYM
UNIVERSITY OF SHEFFIELD SHEFFIELD, UK MICHAELJ. CLOUD LAWRENCE
TECHNOLOGICAL UNIVERSITY SOUTHFIELD, USA 2005 ELSEVIER AMSTERDAM -
BOSTON - HEIDELBERG - LONDON - NEW YORK - OXFORD PARIS - SAN DIEGO - SAN
FRANCISCO - SINGAPORE - SYDNEY - TOKYO CONTENTS PREFACE V
ACKNOWLEDGEMENTS IX CONTENTS XI 1 BANACH SPACES 1 1.1 INTRODUCTION 1 1.2
VECTOR SPACES 3 1.3 NORMED VECTOR SPACES 7 1.4 BANACH SPACES 18 1.5
HILBERT SPACE 27 PROBLEMS 36 2 LEBESGUE INTEGRATION AND THE C P SPACES
39 2.1 INTRODUCTION 39 2.2 THE MEASURE OF A SET 41 2.3 MEASURABLE
FUNCTIONS 48 2.4 INTEGRATION 50 2.5 THE C P SPACES 57 2.6 APPLICATIONS
60 PROBLEMS 62 3 FOUNDATIONS OF LINEAR OPERATOR THEORY 65 3.1
INTRODUCTION 65 3.2 THE BASIC TERMINOLOGY OF OPERATOR THEORY 67 3.3 SOME
ALGEBRAIC PROPERTIES OF LINEAR OPERATORS 69 3.4 CONTINUITY AND
BOUNDEDNESS 74 3.5 SOME FUNDAMENTAL PROPERTIES OF BOUNDED OPERATORS . .
. . 82 3.6 FIRST RESULTS ON THE SOLUTION OF THE EQUATION LF = G . . . .
90 3.7 INTRODUCTION TO SPECTRAL THEORY 96 XI XII CONTENTS 3.8 CLOSED
OPERATORS AND DIFFERENTIAL EQUATIONS 101 PROBLEMS 108 4 INTRODUCTION TO
NONLINEAR OPERATORS 115 4.1 INTRODUCTION 115 4.2 PRELIMINARIES 117 4.3
THE CONTRACTION MAPPING PRINCIPLE 121 4.4 THE FRECHET DERIVATIVE 130 4.5
NEWTON S METHOD FOR NONLINEAR OPERATORS 136 PROBLEMS 143 5 COMPACT SETS
IN BANACH SPACES 147 5.1 INTRODUCTION 147 5.2 DEFINITIONS 148 5.3 SOME
CONSEQUENCES OF COMPACTNESS 150 5.4 SOME IMPORTANT COMPACT SETS OF
FUNCTIONS 153 PROBLEMS 155 6 THE ADJOINT OPERATOR 157 6.1 INTRODUCTION
157 6.2 THE DUAL OF A BANACH SPACE 158 6.3 WEAK CONVERGENCE 165 6.4
HILBERT SPACE 168 6.5 THE ADJOINT OF A BOUNDED LINEAR OPERATOR 170 6.6
BOUNDED SELF-ADJOINT OPERATORS * SPECTRAL THEORY 175 6.7 THE ADJOINT OF
AN UNBOUNDED LINEAR OPERATOR IN HILBERT SPACE 179 PROBLEMS 184 7 LINEAR
COMPACT OPERATORS 189 7.1 INTRODUCTION 189 7.2 EXAMPLES OF COMPACT
OPERATORS 190 7.3 THE FREDHOLM ALTERNATIVE 195 7.4 THE SPECTRUM 199 7.5
COMPACT SELF-ADJOINT OPERATORS 202 7.6 THE NUMERICAL SOLUTION OF LINEAR
INTEGRAL EQUATIONS . . . . 205 PROBLEMS 212 8 NONLINEAR COMPACT
OPERATORS AND MONOTONICITY 217 8.1 INTRODUCTION 217 8.2 THE SCHAUDER
FIXED POINT THEOREM ,-220 XM 8.3 POSITIVE AND MONOTONE OPERATORS IN
PARTIALLY ORDERED BA- NACH SPACES 224 PROBLEMS 236 9 THE SPECTRAL
THEOREM 241 9.1 INTRODUCTION 241 9.2 PRELIMINARIES 243 9.3 BACKGROUND TO
THE SPECTRAL THEOREM 250 9.4 THE SPECTRAL THEOREM FOR BOUNDED
SELF-ADJOINT OPERATORS . 254 9.5 THE SPECTRUM AND THE RESOLVENT 258 9.6
UNBOUNDED SELF-ADJOINT OPERATORS 262 9.7 THE SOLUTION OF AN EVOLUTION
EQUATION 264 PROBLEMS 266 10 GENERALIZED EIGENFUNCTION EXPANSIONS
ASSOCIATED WITH ORDINARY DIFFERENTIAL EQUATIONS 269 10.1 INTRODUCTION
269 10.2 EXTENSIONS OF SYMMETRIC OPERATORS 271 10.3 FORMAL ORDINARY
DIFFERENTIAL OPERATORS: PRELIMINARIES . . . 278 10.4 SYMMETRIC OPERATORS
ASSOCIATED WITH FORMAL ORDINARY DIF- FERENTIAL OPERATORS 280 10.5 THE
CONSTRUCTION OF SELF-ADJOINT EXTENSIONS 285 10.6 GENERALIZED
EIGENFUNCTION EXPANSIONS 292 PROBLEMS 299 11 LINEAR ELLIPTIC PARTIAL
DIFFERENTIAL EQUATIONS 303 11.1 INTRODUCTION 303 11.2 NOTATION 305 11.3
WEAK DERIVATIVES AND SOBOLEV SPACES 308 11.4 THE GENERALIZED DIRICHLET
PROBLEM 318 11.5 FREDHOLM ALTERNATIVE FOR GENERALIZED DIRICHLET PROBLEM
. . 324 11.6 SMOOTHNESS OF WEAK SOLUTIONS 327 11.7 FURTHER DEVELOPMENTS
336 PROBLEMS 338 12 THE FINITE ELEMENT METHOD 343 12.1 INTRODUCTION 343
12.2 THE RITZ METHOD 344 12.3 THE RATE OF CONVERGENCE OF THE FINITE
ELEMENT METHOD . . 351 PROBLEMS 356 XIV CONTENTS 13 INTRODUCTION TO
DEGREE THEORY 359 13.1 INTRODUCTION 359 13.2 THE DEGREE IN FINITE
DIMENSIONS 365 13.3 THE LERAY-SCHAUDER DEGREE 373 13.4 A PROBLEM IN
RADIATIVE TRANSFER 377 PROBLEMS 381 14 BIFURCATION THEORY 385 14.1
INTRODUCTION 385 14.2 LOCAL BIFURCATION THEORY 388 14.3 GLOBAL
EIGENFUNCTION THEORY 395 PROBLEMS 406 REFERENCES 409 LIST OF SYMBOLS 417
INDEX 421
|
| any_adam_object | 1 |
| author | Hutson, Vivian Pym, John S. Cloud, Michael J. 1960- |
| author_GND | (DE-588)120264242 |
| author_facet | Hutson, Vivian Pym, John S. Cloud, Michael J. 1960- |
| author_role | aut aut aut |
| author_sort | Hutson, Vivian |
| author_variant | v h vh j s p js jsp m j c mj mjc |
| building | Verbundindex |
| bvnumber | BV021484815 |
| callnumber-first | Q - Science |
| callnumber-label | QA320 |
| callnumber-raw | QA320 |
| callnumber-search | QA320 |
| callnumber-sort | QA 3320 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)57373730 (DE-599)BVBBV021484815 |
| dewey-full | 515/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7 |
| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021484815 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T19:14:58Z |
| institution | BVB |
| isbn | 0444517901 |
| language | English |
| lccn | 2004066187 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014683737 |
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| owner | DE-92 DE-824 DE-634 DE-83 |
| owner_facet | DE-92 DE-824 DE-634 DE-83 |
| physical | XIV, 426 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Elsevier |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spellingShingle | Hutson, Vivian Pym, John S. Cloud, Michael J. 1960- Applications of functional analysis and operator theory Mathematics in science and engineering Análisis funcional lemb Functional analysis Operator theory Anwendung (DE-588)4196864-5 gnd Operator (DE-588)4130529-2 gnd Funktionalanalysis (DE-588)4018916-8 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4130529-2 (DE-588)4018916-8 (DE-588)4075665-8 |
| title | Applications of functional analysis and operator theory |
| title_auth | Applications of functional analysis and operator theory |
| title_exact_search | Applications of functional analysis and operator theory |
| title_full | Applications of functional analysis and operator theory Vivian Hutson, John S. Pym, Michael J. Cloud |
| title_fullStr | Applications of functional analysis and operator theory Vivian Hutson, John S. Pym, Michael J. Cloud |
| title_full_unstemmed | Applications of functional analysis and operator theory Vivian Hutson, John S. Pym, Michael J. Cloud |
| title_short | Applications of functional analysis and operator theory |
| title_sort | applications of functional analysis and operator theory |
| topic | Análisis funcional lemb Functional analysis Operator theory Anwendung (DE-588)4196864-5 gnd Operator (DE-588)4130529-2 gnd Funktionalanalysis (DE-588)4018916-8 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Análisis funcional Functional analysis Operator theory Anwendung Operator Funktionalanalysis Operatortheorie |
| url | http://catdir.loc.gov/catdir/enhancements/fy0619/2004066187-d.html http://www.gbv.de/dms/goettingen/474734862.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014683737&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001196 |
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