Hilbert spaces with applications:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2005
|
| Edition: | 3. ed |
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Früh. Aufl. u.d.T.: Debnath, Lokenath: Introduction to Hilbert spaces with applications Nebentitel: Introduction to Hilbert spaces with applications Literaturangaben |
| Physical Description: | XVIII, 580 S. graph. Darst. |
| ISBN: | 0122084381 9780122084386 |
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Record in the Search Index
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| adam_text | HILBERT SPACES WITH APPLICATIONS THIRD EDITION LOKENATH DEBNATH
UNIVERSITY OF TEXAS * PAN AMERICAN PIOTR MIKUSINSKI UNIVERSITY OF
CENTRAL FLORIDA ELSEVIER ACADEMIC PRESS AMSTERDAM * BOSTON * HEIDELBERG
* LONDON * NEW YORK * OXFORD * PARIS * SAN DIEGO * SAN FRANCISCO *
SINGAPORE * SYDNEY * TOKYO CONTENTS PREFACE TO THE THIRD EDITION XI
PREFACE TO THE SECOND EDITION XIII PREFACE TO THE FIRST EDITION XV
CHAPTER L NORMED VECTOR SPACES 1 1.1 INTRODUCTION 1 1.2 VECTOR SPACES 2
1.3 NORMED SPACES 8 1.4 BANACH SPACES 19 1.5 LINEAR MAPPINGS 25 1.6
CONTRACTION MAPPINGS AND THE BANACH FIXED POINT THEOREM 32 1.7 EXERCISES
34 CHAPTER 2 THE LEBESGUE INTEGRAL 39 2.1 INTRODUCTION 39 2.2 STEP
FUNCTIONS 40 2.3 LEBESGUE INTEGRABLE FUNCTIONS 45 2.4 THE ABSOLUTE VALUE
OF AN INTEGRABLE FUNCTION 48 2.5 SERIES OF INTEGRABLE FUNCTIONS 50 2.6
NORM IN/ (I?:) 52 2.7 CONVERGENCE ALMOST EVERYWHERE 55 2.8 FUNDAMENTAL
CONVERGENCE THEOREMS 58 2.9 LOCALLY INTEGRABLE FUNCTIONS 62 VII VIII
CONTENTS 2.10 THE LEBESGUE INTEGRAL AND THE RIEMANN INTEGRAL 64 2.11
LEBESGUE MEASURE ON M. 67 2.12 COMPLEX-VALUED LEBESGUE INTEGRABLE
FUNCTIONS 71 2.13 THE SPACES L?(R) 74 2.14 LEBESGUE INTEGRABLE FUNCTIONS
ON M. N 78 2.15 CONVOLUTION 82 2.16 EXERCISES 84 CHAPTER 3 HILBERT
SPACES AND ORTHONORMAL SYSTEMS 93 3.1 INTRODUCTION 93 3.2 INNER PRODUCT
SPACES 94 3.3 HILBERT SPACES 99 3.4 ORTHOGONAL AND ORTHONORMAL SYSTEMS
105 3.5 TRIGONOMETRIC FOURIER SERIES 122 3.6 ORTHOGONAL COMPLEMENTS AND
PROJECTIONS 127 3.7 LINEAR FUNCTIONALS AND THE RIESZ REPRESENTATION
THEOREM 132 3.8 EXERCISES 135 CHAPTER 4 LINEAR OPERATORS ON HILBERT
SPACES 145 4.1 INTRODUCTION 145 4.2 EXAMPLES OF OPERATORS 146 4.3
BILINEAR FUNCTIONALS AND QUADRATIC FORMS 151 4.4 ADJOINT AND
SELF-ADJOINT OPERATORS 158 4.5 INVERTIBLE, NORMAL, ISOMETRIC, AND
UNITARY OPERATORS 163 4.6 POSITIVE OPERATORS 168 4.7 PROJECTION
OPERATORS 175 4.8 COMPACT OPERATORS 180 4.9 EIGENVALUES AND EIGENVECTORS
186 4.10 SPECTRAL DECOMPOSITION 196 4.11 UNBOUNDED OPERATORS 201 4.12
EXERCISES 211 CHAPTER 5 APPLICATIONS TO INTEGRAL AND DIFFERENTIAL
EQUATIONS 217 5.1 INTRODUCTION 217 5.2 BASIC EXISTENCE THEOREMS 218 5.3
FREDHOLM INTEGRAL EQUATIONS 224 5.4 METHOD OF SUCCESSIVE APPROXIMATIONS
226 5.5 VOLTERRA INTEGRAL EQUATIONS 228 CONTENTS IX 5.6 METHOD OF
SOLUTION FOR A SEPARABLE KERNEL 233 5.7 VOLTERRA INTEGRAL EQUATIONS OF
THE FIRST KIND AND ABEL S INTEGRAL EQUATION 236 5.8 ORDINARY
DIFFERENTIAL EQUATIONS AND DIFFERENTIAL OPERATORS 239 5.9
STURM-LIOUVILLE SYSTEMS 247 5.10 INVERSE DIFFERENTIAL OPERATORS AND
GREEN S FUNCTIONS 253 5.11 THE FOURIER TRANSFORM 258 5.12 APPLICATIONS
OF THE FOURIER TRANSFORM TO ORDINARY DIFFERENTIAL EQUATIONS AND INTEGRAL
EQUATIONS 271 5.13 EXERCISES 279 CHAPTER 6 GENERALIZED FUNCTIONS AND
PARTIAL DIFFERENTIAL EQUATIONS 287 6.1 INTRODUCTION 287 6.2
DISTRIBUTIONS 288 6.3 SOBOLEV SPACES 300 6.4 FUNDAMENTAL SOLUTIONS AND
GREEN S FUNCTIONS FOR PARTIAL DIFFERENTIAL EQUATIONS 303 6.5 WEAK
SOLUTIONS OF ELLIPTIC BOUNDARY VALUE PROBLEMS 323 6.6 EXAMPLES OF
APPLICATIONS OF THE FOURIER TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS
329 6.7 EXERCISES 343 CHAPTER 7 MATHEMATICAL FOUNDATIONS OF QUANTUM
MECHANICS 351 7.1 INTRODUCTION 351 7.2 BASIC CONCEPTS AND EQUATIONS OF
CLASSICAL MECHANICS 352 POISSON S BRACKETS IN MECHANICS 361 7.3 BASIC
CONCEPTS AND POSTULATES OF QUANTUM MECHANICS 363 7.4 THE HEISENBERG
UNCERTAINTY PRINCIPLE 377 7.5 THE SCHRODINGER EQUATION OF MOTION 379 7.6
THE SCHRODINGER PICTURE 395 7.7 THE HEISENBERG PICTURE AND THE
HEISENBERG EQUATION OF MOTION 401 7.8 THE INTERACTION PICTURE 405 7.9
THE LINEAR HARMONIC OSCILLATOR 407 7.10 ANGULAR MOMENTUM OPERATORS 412
7.11 THE DIRAC RELATIVISTIC WAVE EQUATION 420 7.12 EXERCISES 423 X
CONTENTS CHAPTER 8 WAVELETS AND WAVELET TRANSFORMS 433 8.1 BRIEF
HISTORICAL REMARKS 433 8.2 CONTINUOUS WAVELET TRANSFORMS 436 8.3 THE
DISCRETE WAVELET TRANSFORM 444 8.4 MULTIRESOLUTION ANALYSIS AND
ORTHONORMAL BASES OF WAVELETS 452 8.5 EXAMPLES OF ORTHONORMAL WAVELETS
462 8.6 EXERCISES 473 CHAPTER 9 OPTIMIZATION PROBLEMS AND OTHER
MISCELLANEOUS APPLICATIONS 477 9.1 INTRODUCTION 477 9.2 THE GATEAUX AND
FRECHET DIFFERENTIALS 478 9.3 OPTIMIZATION PROBLEMS AND THE
EULER-LAGRANGE EQUATIONS 490 9.4 MINIMIZATION OF QUADRATIC FUNCTIONALS
505 9.5 VARIATIONAL INEQUALITIES 507 9.6 OPTIMAL CONTROL PROBLEMS FOR
DYNAMICAL SYSTEMS 510 9.7 APPROXIMATION THEORY 517 9.8 THE SHANNON
SAMPLING THEOREM 522 9.9 LINEAR AND NONLINEAR STABILITY 526 9.10
BIFURCATION THEORY 530 9.11 EXERCISES 535 HINTS AND ANSWERS TO SELECTED
EXERCISES 547 BIBLIOGRAPHY B65 INDEX 571
|
| adam_txt |
HILBERT SPACES WITH APPLICATIONS THIRD EDITION LOKENATH DEBNATH
UNIVERSITY OF TEXAS * PAN AMERICAN PIOTR MIKUSINSKI UNIVERSITY OF
CENTRAL FLORIDA ELSEVIER ACADEMIC PRESS AMSTERDAM * BOSTON * HEIDELBERG
* LONDON * NEW YORK * OXFORD * PARIS * SAN DIEGO * SAN FRANCISCO *
SINGAPORE * SYDNEY * TOKYO CONTENTS PREFACE TO THE THIRD EDITION XI
PREFACE TO THE SECOND EDITION XIII PREFACE TO THE FIRST EDITION XV
CHAPTER L NORMED VECTOR SPACES 1 1.1 INTRODUCTION 1 1.2 VECTOR SPACES 2
1.3 NORMED SPACES 8 1.4 BANACH SPACES 19 1.5 LINEAR MAPPINGS 25 1.6
CONTRACTION MAPPINGS AND THE BANACH FIXED POINT THEOREM 32 1.7 EXERCISES
34 CHAPTER 2 THE LEBESGUE INTEGRAL 39 2.1 INTRODUCTION 39 2.2 STEP
FUNCTIONS 40 2.3 LEBESGUE INTEGRABLE FUNCTIONS 45 2.4 THE ABSOLUTE VALUE
OF AN INTEGRABLE FUNCTION 48 2.5 SERIES OF INTEGRABLE FUNCTIONS 50 2.6
NORM IN/'(I?:) 52 2.7 CONVERGENCE ALMOST EVERYWHERE 55 2.8 FUNDAMENTAL
CONVERGENCE THEOREMS 58 2.9 LOCALLY INTEGRABLE FUNCTIONS 62 VII VIII
CONTENTS 2.10 THE LEBESGUE INTEGRAL AND THE RIEMANN INTEGRAL 64 2.11
LEBESGUE MEASURE ON M. 67 2.12 COMPLEX-VALUED LEBESGUE INTEGRABLE
FUNCTIONS 71 2.13 THE SPACES L?(R) 74 2.14 LEBESGUE INTEGRABLE FUNCTIONS
ON M. N 78 2.15 CONVOLUTION 82 2.16 EXERCISES 84 CHAPTER 3 HILBERT
SPACES AND ORTHONORMAL SYSTEMS 93 3.1 INTRODUCTION 93 3.2 INNER PRODUCT
SPACES 94 3.3 HILBERT SPACES 99 3.4 ORTHOGONAL AND ORTHONORMAL SYSTEMS
105 3.5 TRIGONOMETRIC FOURIER SERIES 122 3.6 ORTHOGONAL COMPLEMENTS AND
PROJECTIONS 127 3.7 LINEAR FUNCTIONALS AND THE RIESZ REPRESENTATION
THEOREM 132 3.8 EXERCISES 135 CHAPTER 4 LINEAR OPERATORS ON HILBERT
SPACES 145 4.1 INTRODUCTION 145 4.2 EXAMPLES OF OPERATORS 146 4.3
BILINEAR FUNCTIONALS AND QUADRATIC FORMS 151 4.4 ADJOINT AND
SELF-ADJOINT OPERATORS 158 4.5 INVERTIBLE, NORMAL, ISOMETRIC, AND
UNITARY OPERATORS 163 4.6 POSITIVE OPERATORS 168 4.7 PROJECTION
OPERATORS 175 4.8 COMPACT OPERATORS 180 4.9 EIGENVALUES AND EIGENVECTORS
186 4.10 SPECTRAL DECOMPOSITION 196 4.11 UNBOUNDED OPERATORS 201 4.12
EXERCISES 211 CHAPTER 5 APPLICATIONS TO INTEGRAL AND DIFFERENTIAL
EQUATIONS 217 5.1 INTRODUCTION 217 5.2 BASIC EXISTENCE THEOREMS 218 5.3
FREDHOLM INTEGRAL EQUATIONS 224 5.4 METHOD OF SUCCESSIVE APPROXIMATIONS
226 5.5 VOLTERRA INTEGRAL EQUATIONS 228 CONTENTS IX 5.6 METHOD OF
SOLUTION FOR A SEPARABLE KERNEL 233 5.7 VOLTERRA INTEGRAL EQUATIONS OF
THE FIRST KIND AND ABEL'S INTEGRAL EQUATION 236 5.8 ORDINARY
DIFFERENTIAL EQUATIONS AND DIFFERENTIAL OPERATORS 239 5.9
STURM-LIOUVILLE SYSTEMS 247 5.10 INVERSE DIFFERENTIAL OPERATORS AND
GREEN'S FUNCTIONS 253 5.11 THE FOURIER TRANSFORM 258 5.12 APPLICATIONS
OF THE FOURIER TRANSFORM TO ORDINARY DIFFERENTIAL EQUATIONS AND INTEGRAL
EQUATIONS 271 5.13 EXERCISES 279 CHAPTER 6 GENERALIZED FUNCTIONS AND
PARTIAL DIFFERENTIAL EQUATIONS 287 6.1 INTRODUCTION 287 6.2
DISTRIBUTIONS 288 6.3 SOBOLEV SPACES 300 6.4 FUNDAMENTAL SOLUTIONS AND
GREEN'S FUNCTIONS FOR PARTIAL DIFFERENTIAL EQUATIONS 303 6.5 WEAK
SOLUTIONS OF ELLIPTIC BOUNDARY VALUE PROBLEMS 323 6.6 EXAMPLES OF
APPLICATIONS OF THE FOURIER TRANSFORM TO PARTIAL DIFFERENTIAL EQUATIONS
329 6.7 EXERCISES 343 CHAPTER 7 MATHEMATICAL FOUNDATIONS OF QUANTUM
MECHANICS 351 7.1 INTRODUCTION 351 7.2 BASIC CONCEPTS AND EQUATIONS OF
CLASSICAL MECHANICS 352 POISSON'S BRACKETS IN MECHANICS 361 7.3 BASIC
CONCEPTS AND POSTULATES OF QUANTUM MECHANICS 363 7.4 THE HEISENBERG
UNCERTAINTY PRINCIPLE 377 7.5 THE SCHRODINGER EQUATION OF MOTION 379 7.6
THE SCHRODINGER PICTURE 395 7.7 THE HEISENBERG PICTURE AND THE
HEISENBERG EQUATION OF MOTION 401 7.8 THE INTERACTION PICTURE 405 7.9
THE LINEAR HARMONIC OSCILLATOR 407 7.10 ANGULAR MOMENTUM OPERATORS 412
7.11 THE DIRAC RELATIVISTIC WAVE EQUATION 420 7.12 EXERCISES 423 X
CONTENTS CHAPTER 8 WAVELETS AND WAVELET TRANSFORMS 433 8.1 BRIEF
HISTORICAL REMARKS 433 8.2 CONTINUOUS WAVELET TRANSFORMS 436 8.3 THE
DISCRETE WAVELET TRANSFORM 444 8.4 MULTIRESOLUTION ANALYSIS AND
ORTHONORMAL BASES OF WAVELETS 452 8.5 EXAMPLES OF ORTHONORMAL WAVELETS
462 8.6 EXERCISES 473 CHAPTER 9 OPTIMIZATION PROBLEMS AND OTHER
MISCELLANEOUS APPLICATIONS 477 9.1 INTRODUCTION 477 9.2 THE GATEAUX AND
FRECHET DIFFERENTIALS 478 9.3 OPTIMIZATION PROBLEMS AND THE
EULER-LAGRANGE EQUATIONS 490 9.4 MINIMIZATION OF QUADRATIC FUNCTIONALS
505 9.5 VARIATIONAL INEQUALITIES 507 9.6 OPTIMAL CONTROL PROBLEMS FOR
DYNAMICAL SYSTEMS 510 9.7 APPROXIMATION THEORY 517 9.8 THE SHANNON
SAMPLING THEOREM 522 9.9 LINEAR AND NONLINEAR STABILITY 526 9.10
BIFURCATION THEORY 530 9.11 EXERCISES 535 HINTS AND ANSWERS TO SELECTED
EXERCISES 547 BIBLIOGRAPHY B65 INDEX 571 |
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| id | DE-604.BV022966591 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:06:54Z |
| indexdate | 2024-07-09T21:08:46Z |
| institution | BVB |
| isbn | 0122084381 9780122084386 |
| language | English |
| lccn | 005284016 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016170900 |
| oclc_num | 61702121 |
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| owner | DE-706 |
| owner_facet | DE-706 |
| physical | XVIII, 580 S. graph. Darst. |
| publishDate | 2005 |
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| publisher | Elsevier |
| record_format | marc |
| spelling | Debnath, Lokenath 1935- Verfasser (DE-588)115600663 aut Hilbert spaces with applications Lokenath Debnath ; Piotr Mikusiński Introduction to Hilbert spaces with applications 3. ed Amsterdam [u.a.] Elsevier 2005 XVIII, 580 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Früh. Aufl. u.d.T.: Debnath, Lokenath: Introduction to Hilbert spaces with applications Nebentitel: Introduction to Hilbert spaces with applications Literaturangaben Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s DE-604 Mikusiński, Piotr Verfasser (DE-588)12359944X aut http://www.loc.gov/catdir/enhancements/fy0627/2005284016-d.html Publisher description lizenzfrei http://www.loc.gov/catdir/toc/fy0604/2005284016.html lizenzfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016170900&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Debnath, Lokenath 1935- Mikusiński, Piotr Hilbert spaces with applications Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4159850-7 |
| title | Hilbert spaces with applications |
| title_alt | Introduction to Hilbert spaces with applications |
| title_auth | Hilbert spaces with applications |
| title_exact_search | Hilbert spaces with applications |
| title_exact_search_txtP | Hilbert spaces with applications |
| title_full | Hilbert spaces with applications Lokenath Debnath ; Piotr Mikusiński |
| title_fullStr | Hilbert spaces with applications Lokenath Debnath ; Piotr Mikusiński |
| title_full_unstemmed | Hilbert spaces with applications Lokenath Debnath ; Piotr Mikusiński |
| title_short | Hilbert spaces with applications |
| title_sort | hilbert spaces with applications |
| topic | Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Hilbert space Hilbert-Raum |
| url | http://www.loc.gov/catdir/enhancements/fy0627/2005284016-d.html http://www.loc.gov/catdir/toc/fy0604/2005284016.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016170900&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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