Holdings: Applications of functional analysis and operator theory

Applications of functional analysis and operator theory:

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Bibliographic Details
Main Authors:	Hutson, Vivian (Author), Pym, John S. (Author), Cloud, Michael J. 1960- (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Elsevier 2005
Edition:	2. ed.
Series:	Mathematics in science and engineering 200
Subjects:	Análisis funcional Functional analysis Operator theory Anwendung Operator Funktionalanalysis Operatortheorie
Online Access:	Beschreibung für Leser Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	XIV, 426 S. graph. Darst.
ISBN:	0444517901

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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
adam_txt	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
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series	Mathematics in science and engineering
series2	Mathematics in science and engineering
spelling	Hutson, Vivian Verfasser aut Applications of functional analysis and operator theory Vivian Hutson, John S. Pym, Michael J. Cloud 2. ed. Amsterdam [u.a.] Elsevier 2005 XIV, 426 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 200 Análisis funcional lemb Functional analysis Operator theory Anwendung (DE-588)4196864-5 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s Anwendung (DE-588)4196864-5 s 1\p DE-604 Operatortheorie (DE-588)4075665-8 s 2\p DE-604 Operator (DE-588)4130529-2 s 3\p DE-604 Pym, John S. Verfasser aut Cloud, Michael J. 1960- Verfasser (DE-588)120264242 aut Mathematics in science and engineering 200 (DE-604)BV000001196 200 http://catdir.loc.gov/catdir/enhancements/fy0619/2004066187-d.html Beschreibung für Leser http://www.gbv.de/dms/goettingen/474734862.pdf Inhaltsverzeichnis GBV Datenaustausch application/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 Inhaltsverzeichnis 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	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_exact_search_txtP	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
work_keys_str_mv	AT hutsonvivian applicationsoffunctionalanalysisandoperatortheory AT pymjohns applicationsoffunctionalanalysisandoperatortheory AT cloudmichaelj applicationsoffunctionalanalysisandoperatortheory

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