Introduction to functional analysis with applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Tunbridge Wells [u.a.]
Anshan [u.a.]
2006
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [351] - 358 |
| Physical Description: | XVII, 362 S. graph. Darst. 25 cm |
| ISBN: | 1904798918 |
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| 246 | 1 | 3 | |a Functional analysis with applications |
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Record in the Search Index
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| adam_text | INTRODUCTION TO FUNCTIONAL ANALYSIS WITH APPLICATIONS A.H. SIDDIQI
KHALIL AHMAD P. MANCHANDA TUNBRIDGE WELLS, UK ANAMAYA PUBLISHERS NEW
DELHI CONTENTS PREFACE VII LIST OF SYMBOLS .: - IX 1. NORMED AND
BANACH SPACES 1 1.1 BASIC DEFINITIONS AND PROPERTIES 1 1.2 EXAMPLES OF
NORMED SPACES AND RELATED CONCEPTS 6 NORMED SPACES 6 BANACH SPACES 13
DIMENSION OF NORMED SPACES 13 OPEN AND CLOSED SPHERES 13 NORMED
SUBSPACES 16 COMPLETION OF NORMED SPACES 16 ISOMETRY AND ISOMORPHISM 16
1.3 OPERATORS AND FUNCTIONALS 17 DEFINITIONS AND EXAMPLES 17 PROPERTIES
OF LINEAR OPERATORS AND DUAL SPACE 25 ALGEBRA OF OPERATORS 32 1.4 CONVEX
FUNCTIONALS (REAL-VALUED CONVEX FUNCTIONS ON NORMED SPACES) 38 CONVEX
SETS 38 AFFINE OPERATOR 40 CONVEX FUNCTIONALS 40 LOWER SEMICONTINUOUS
(LSC) AND UPPER SEMICONTINUOUS (USE) FUNCTIONALS 43 1.5 TOPOLOGICAL
PROPERTIES OF NORMED SPACES 44 COMPACTNESS IN NORMED SPACES 44
SEPARABILITY AND CONNECTEDNESS FOR NORMED SPACES 49 EQUIVALENT NORMS AND
FINITE-DIMENSIONAL SPACES SO REFLEXIVE NORMED SPACES AND DIFFERENT KINDS
OF TOPOLOGIES 53 NORME D SPACES WITH BASIS OR BASE 54 1.6 GEOMETRICAL
PROPERTIES OF NORMED SPACES 55 1.7 SOME MORE EXAMPLES 56 EXERCISES 75
SOLUTIONS TO EXERCISES 77 2. INNER PRODUCT AND HILBERT SPACES : 81 2.1
BASIC DEFINITIONS AND PROPERTIES 81 DEFINITIONS, EXAMPLES AND PROPERTIES
OF INNER-PRODUCT SPACE 81 XIV CONTENTS HILBERT SPACE 86 PARALLELOGRAM
LAW AND CHARACTERIZATION OF HILBERT SPACE 87 2.2 ORTHOGONAL COMPLEMENTS
AND PROJECTION THEOREM 93 ORTHOGONAL COMPLEMENTS AND PROJECTIONS 93
PROJECTION THEOREM 95 2.3 ORTHONORMAL SYSTEMS AND FOURIER EXPANSION 100
DEFINITIONS, EXAMPLES AND GRAM-SCHMIDT ORTHOGONALIZATION -** PROCESS 100
BESSEL S INEQUALITY 104 2.4 DUALITY AND REFLEXIVITY 106 RIESZ
REPRESENTATION THEOREM 106 REFLEXIVITY OF HILBERT SPACES 109 2.5
OPERATORS IN HILBERT SPACE 110 ADJOINT OF A BOUNDED LINEAR OPERATOR ON A
HILBERT SPACE 110 SELF-ADJOINT, POSITIVE, NORMAL AND UNITARY OPERATORS
115 ADJOINT OF AN UNBOUNDED LINEAR OPERATOR 122 2.6 BILINEAR FORMS AND
LAX-MILGRARRI LEMMA 124 2.7 PROJECTION ON CONVEX SETS 131 2.8 SOME MORE
EXAMPLES 134 EXERCISES 144 SOLUTIONS TO EXERCISES 146 3. FUNDAMENTAL
THEOREMS 149 3.1 EXTENSION FORM OF THE HAHN-BANACH THEOREM AND ITS
CONSEQUENCES 149 CONSEQUENCES OF THE EXTENSION FORM OF THE HAHN-BANACH
THEOREM 154 3.2 GEOMETRIC FORM OF THE HAHN-BANACH THEOREM AND ITS
COROLLARIES 157 3.3 PRINCIPLE OF UNIFORM BOUNDEDNESS AND ITS
APPLICATIONS 159 PRINCIPLE OF UNIFORM BOUNDEDNESS 159 APPLICATIONS OF
THE PRINCIPLE OF UNIFORM BOUNDEDNESS IN FOURIER ANALYSIS 160 3.4 OPEN
MAPPING AND CLOSED GRAPH THEOREMS 162 GRAPH OF A LINEAR OPERATOR AND
CLOSEDNESS PROPERTY 162 OPEN MAPPING THEOREM 164 CLOSED GRAPH THEOREM
165 3.5 EXAMPLES 166 EXERCISES 168 SOLUTIONS TO EXERCISES 169 4. WEAK
TOPOLOGIES, WEAK CONVERGENCE AND REFLEXIVE SPACES 170 4.1 WEAK
TOPOLOGIES 170 4.2 WEAK CONVERGENCE 171 4.3 REFLEXIVE BANACH SPACES 173
: CONTENTS XV 4.4 WEAK CONVERGENCE IN HILBERT SPACES 174 4.5 EXAMPLES
176 EXERCISES 178 SOLUTIONS TO EXERCISES 178 5. DIFFERENTIATION AND
INTEGRATION IN NORMED SPACES 180 5.1 GATEAUX DERIVATIVE 180 5.2 FRECHET
DERIVATIVE 183 5.3 SUBDIFFERENTIAL 186 5.4 INTEGRATION IN NORMED SPACES
188 EXERCISES 189 SOLUTIONS TO EXERCISES 190 6. FIXED-POINT THEOREMS AND
THEIR APPLICATIONS 191 6.1 BANACH CONTRACTION PRINCIPLE AND ITS
GENERALIZATIONS 191 6.2 SCHAUDER S FIXED-POINT THEOREM 195 6.3
APPLICATIONS OF BANACH CONTRACTION PRINCIPLE 196 APPLICATION TO MATRIX
EQUATION 196 APPLICATION TO DIFFERENTIAL EQUATIONS 201 EXERCISES 203
SOLUTIONS TO EXERCISES 206 7. RUDIMENTS OF SPECTRAL THEORY 210 7.1
SPECTRAL PROPERTIES OF BOUNDED LINEAR OPERATORS 210 7.2 COMPACT
OPERATORS 211 7.3 SPECTRAL PROPERTIES OF SELF-ADJOINT AND COMPACT
OPERATORS 215 7.4 SPECTRAL DECOMPOSITION 216 SOLVABILITY OF OPERATOR
EQUATIONS 219 CHARACTERIZATION OF SOLVABILITY IN TERMS OF RANGE AND NULL
SPACES 222 CHARACTERIZATION OF LAX-MILGRAM LEMMA 223 EXISTENCE THEOREM
FOR NONLINEAR OPERATORS 224 7.5 EXAMPLES 225 EXERCISES 226 SOLUTIONS TO
EXERCISES 227 8. BOUNDARY VALUE PROBLEMS 230 8.1 DEFINITION AND EXAMPLES
OF BOUNDARY VALUE PROBLEMS 230 DEFINITION 230 EXAMPLES OF BVPS 231 8.2
ABSTRACT EQUATIONS 236 8.3 SOBOLEV SPACE 238 EXAMPLES OF DISTRIBUTION
239 8.4 CERTAIN REMARKS CONCERNING THE SOLUTIONS OF BVPS 246 XVI
CONTENTS EXERCISES 249 SOLUTIONS TO EXERCISES 249 9. OPTIMIZATION 251
9.1 MINIMIZATION OF FUNCTIONALS 251 9.2 CALCULUS OF VARIATION AND LINEAR
PROGRAMMING -255 CALCULUS OF VARIATION 255 LINEAR PROGRAMMING 257
EXERCISES 257 SOLUTIONS TO EXERCISES 258 10. VARIATIONAL INEQUALITIES
260 10.1 LIONS-STAMPACCHIA THEORY 260 10.2 PHYSICAL PHENOMENA
REPRESENTED BY VARIATIONAL INEQUALITIES 265 EXERCISES 267 SOLUTIONS TO
EXERCISES 267 11. THE FINITE-ELEMENT METHOD 269 11.1 APPROXIMATE PROBLEM
270 11.2 INTERNAL APPROXIMATION OF// (Q) 273 11.3 FINITE ELEMENTS 275
11.4 APPLICATION OF THE FINITE-ELEMENT METHOD TO SOLVE BOUNDARY VALUE
PROBLEMS 279 PRACTICAL METHOD TO COMPUTE A(WJ, W,) 281 11.5 EFFECT OF
NUMERICAL INTEGRATION 281 11.6 ABSTRACT ERROR ESTIMATE FOR THE
NONCONFORMING FINITE-ELEMENT METHOD 284 11.7 ABSTRACT ERROR ESTIMATION
FOR VARIATIONAL INEQUALITIES 285 EXERCISES 286 SOLUTIONS TO EXERCISES
287 12. OPTIMAL CONTROL 288 12.1 PROBLEM ILLUSTRATION WITH THE HELP OF
AN EXAMPLE AND FORMULATION OF GENERAL PROBLEM 289 FORMULATION OF THE
GENERAL OPTIMAL CONTROL PROBLEM FOR A SYSTEM REPRESENTED BY DIFFERENTIAL
EQUATION 290 12.2 LINEAR QUADRATIC CONTROL PROBLEM 291 EXERCISES 297
SOLUTIONS TO EXERCISES 297 13. WAVELETS 298 13.1 RECAPITULATION OF SOME
BASIC CONCEPTS 298 13.2 CONTINUOUS WAVELET TRANSFORM 300 CONTENTS XVII
13.3 EXAMPLES OF WAVELETS 301 13.4 DECAY OF CONTINUOUS WAVELET TRANSFORM
308 13.5 MULTIRESOLUTION ANALYSIS 310 EXAMPLES OF MULTIRESOLUTION
ANALYSIS 311 IMPORTANT PROPERTIES OF MRA 311 13.6 DECOMPOSITION AND
RECONSTRUCTION ALGORITHMS 319 13.7 BESTAF-TERMAPPROXIMATION 320 13.8
WAVELET AND FUNCTION SPACES 322 EXERCISES 322 APPENDIX A 325 APPENDIX B
328 APPENDIX C 331 APPENDIX D 335 APPENDIX E 343 APPENDIX F 345
REFERENCES 351 INDEX 359
|
| adam_txt |
INTRODUCTION TO FUNCTIONAL ANALYSIS WITH APPLICATIONS A.H. SIDDIQI
KHALIL AHMAD P. MANCHANDA TUNBRIDGE WELLS, UK ANAMAYA PUBLISHERS NEW
DELHI CONTENTS PREFACE VII LIST OF SYMBOLS .: ' - IX 1. NORMED AND
BANACH SPACES 1 1.1 BASIC DEFINITIONS AND PROPERTIES 1 1.2 EXAMPLES OF
NORMED SPACES AND RELATED CONCEPTS 6 NORMED SPACES 6 BANACH SPACES 13
DIMENSION OF NORMED SPACES 13 OPEN AND CLOSED SPHERES 13 NORMED
SUBSPACES 16 COMPLETION OF NORMED SPACES 16 ISOMETRY AND ISOMORPHISM 16
1.3 OPERATORS AND FUNCTIONALS 17 DEFINITIONS AND EXAMPLES 17 PROPERTIES
OF LINEAR OPERATORS AND DUAL SPACE 25 ALGEBRA OF OPERATORS 32 1.4 CONVEX
FUNCTIONALS (REAL-VALUED CONVEX FUNCTIONS ON NORMED SPACES) 38 CONVEX
SETS 38 AFFINE OPERATOR 40 CONVEX FUNCTIONALS 40 LOWER SEMICONTINUOUS
(LSC) AND UPPER SEMICONTINUOUS (USE) FUNCTIONALS 43 1.5 TOPOLOGICAL
PROPERTIES OF NORMED SPACES 44 COMPACTNESS IN NORMED SPACES 44
SEPARABILITY AND CONNECTEDNESS FOR NORMED SPACES 49 EQUIVALENT NORMS AND
FINITE-DIMENSIONAL SPACES SO REFLEXIVE NORMED SPACES AND DIFFERENT KINDS
OF TOPOLOGIES 53 NORME'D SPACES WITH BASIS OR BASE 54 1.6 GEOMETRICAL
PROPERTIES OF NORMED SPACES 55 1.7 SOME MORE EXAMPLES 56 EXERCISES 75
SOLUTIONS TO EXERCISES 77 2. INNER PRODUCT AND HILBERT SPACES : 81 2.1
BASIC DEFINITIONS AND PROPERTIES 81 DEFINITIONS, EXAMPLES AND PROPERTIES
OF INNER-PRODUCT SPACE 81 XIV CONTENTS HILBERT SPACE 86 PARALLELOGRAM
LAW AND CHARACTERIZATION OF HILBERT SPACE 87 2.2 ORTHOGONAL COMPLEMENTS
AND PROJECTION THEOREM 93 ORTHOGONAL COMPLEMENTS AND PROJECTIONS 93
PROJECTION THEOREM 95 2.3 ORTHONORMAL SYSTEMS AND FOURIER EXPANSION 100
DEFINITIONS, EXAMPLES AND GRAM-SCHMIDT ORTHOGONALIZATION -** PROCESS 100
BESSEL'S INEQUALITY 104 2.4 DUALITY AND REFLEXIVITY 106 RIESZ
REPRESENTATION THEOREM 106 REFLEXIVITY OF HILBERT SPACES 109 2.5
OPERATORS IN HILBERT SPACE 110 ADJOINT OF A BOUNDED LINEAR OPERATOR ON A
HILBERT SPACE 110 SELF-ADJOINT, POSITIVE, NORMAL AND UNITARY OPERATORS
115 ' ADJOINT OF AN UNBOUNDED LINEAR OPERATOR 122 2.6 BILINEAR FORMS AND
LAX-MILGRARRI LEMMA 124 2.7 PROJECTION ON CONVEX SETS 131 2.8 SOME MORE
EXAMPLES 134 EXERCISES 144 SOLUTIONS TO EXERCISES 146 3. FUNDAMENTAL
THEOREMS 149 3.1 EXTENSION FORM OF THE HAHN-BANACH THEOREM AND ITS
CONSEQUENCES 149 CONSEQUENCES OF THE EXTENSION FORM OF THE HAHN-BANACH
THEOREM 154 3.2 GEOMETRIC FORM OF THE HAHN-BANACH THEOREM AND ITS
COROLLARIES 157 3.3 PRINCIPLE OF UNIFORM BOUNDEDNESS AND ITS
APPLICATIONS 159 PRINCIPLE OF UNIFORM BOUNDEDNESS 159 APPLICATIONS OF
THE PRINCIPLE OF UNIFORM BOUNDEDNESS IN FOURIER ANALYSIS 160 3.4 OPEN
MAPPING AND CLOSED GRAPH THEOREMS 162 GRAPH OF A LINEAR OPERATOR AND
CLOSEDNESS PROPERTY 162 OPEN MAPPING THEOREM 164 CLOSED GRAPH THEOREM
165 3.5 EXAMPLES 166 EXERCISES 168 SOLUTIONS TO EXERCISES 169 4. WEAK
TOPOLOGIES, WEAK CONVERGENCE AND REFLEXIVE SPACES 170 4.1 WEAK
TOPOLOGIES 170 4.2 WEAK CONVERGENCE 171 4.3 REFLEXIVE BANACH SPACES 173
: CONTENTS XV 4.4 WEAK CONVERGENCE IN HILBERT SPACES 174 4.5 EXAMPLES
176 EXERCISES 178 SOLUTIONS TO EXERCISES 178 5. DIFFERENTIATION AND
INTEGRATION IN NORMED SPACES 180 5.1 GATEAUX DERIVATIVE 180 5.2 FRECHET
DERIVATIVE 183 5.3 SUBDIFFERENTIAL 186 5.4 INTEGRATION IN NORMED SPACES
188 EXERCISES 189 SOLUTIONS TO EXERCISES 190 6. FIXED-POINT THEOREMS AND
THEIR APPLICATIONS 191 6.1 BANACH CONTRACTION PRINCIPLE AND ITS
GENERALIZATIONS 191 6.2 SCHAUDER'S FIXED-POINT THEOREM 195 6.3
APPLICATIONS OF BANACH CONTRACTION PRINCIPLE 196 APPLICATION TO MATRIX
EQUATION 196 " APPLICATION TO DIFFERENTIAL EQUATIONS 201 EXERCISES 203
SOLUTIONS TO EXERCISES 206 7. RUDIMENTS OF SPECTRAL THEORY 210 7.1
SPECTRAL PROPERTIES OF BOUNDED LINEAR OPERATORS 210 7.2 COMPACT
OPERATORS 211 7.3 SPECTRAL PROPERTIES OF SELF-ADJOINT AND COMPACT
OPERATORS 215 7.4 SPECTRAL DECOMPOSITION 216 SOLVABILITY OF OPERATOR
EQUATIONS 219 CHARACTERIZATION OF SOLVABILITY IN TERMS OF RANGE AND NULL
SPACES 222 CHARACTERIZATION OF LAX-MILGRAM LEMMA 223 EXISTENCE THEOREM
FOR NONLINEAR OPERATORS 224 7.5 EXAMPLES 225 EXERCISES 226 SOLUTIONS TO
EXERCISES 227 8. BOUNDARY VALUE PROBLEMS 230 8.1 DEFINITION AND EXAMPLES
OF BOUNDARY VALUE PROBLEMS 230 DEFINITION 230 EXAMPLES OF BVPS 231 8.2
ABSTRACT EQUATIONS 236 8.3 SOBOLEV SPACE 238 EXAMPLES OF DISTRIBUTION
239 8.4 CERTAIN REMARKS CONCERNING THE SOLUTIONS OF BVPS 246 XVI
CONTENTS EXERCISES 249 SOLUTIONS TO EXERCISES 249 9. OPTIMIZATION 251
9.1 MINIMIZATION OF FUNCTIONALS 251 9.2 CALCULUS OF VARIATION AND LINEAR
PROGRAMMING -255 CALCULUS OF VARIATION 255 LINEAR PROGRAMMING 257
EXERCISES 257 SOLUTIONS TO EXERCISES 258 10. VARIATIONAL INEQUALITIES
260 10.1 LIONS-STAMPACCHIA THEORY 260 10.2 PHYSICAL PHENOMENA
REPRESENTED BY VARIATIONAL INEQUALITIES 265 EXERCISES 267 SOLUTIONS TO
EXERCISES 267 11. THE FINITE-ELEMENT METHOD 269 11.1 APPROXIMATE PROBLEM
270 11.2 INTERNAL APPROXIMATION OF//'(Q) 273 11.3 FINITE ELEMENTS 275
11.4 APPLICATION OF THE FINITE-ELEMENT METHOD TO SOLVE BOUNDARY VALUE
PROBLEMS 279 PRACTICAL METHOD TO COMPUTE A(WJ, W,) 281 11.5 EFFECT OF
NUMERICAL INTEGRATION 281 11.6 ABSTRACT ERROR ESTIMATE FOR THE
NONCONFORMING FINITE-ELEMENT METHOD 284 11.7 ABSTRACT ERROR ESTIMATION
FOR VARIATIONAL INEQUALITIES 285 EXERCISES 286 SOLUTIONS TO EXERCISES
287 12. OPTIMAL CONTROL 288 12.1 PROBLEM ILLUSTRATION WITH THE HELP OF
AN EXAMPLE AND FORMULATION OF GENERAL PROBLEM 289 FORMULATION OF THE
GENERAL OPTIMAL CONTROL PROBLEM FOR A SYSTEM REPRESENTED BY DIFFERENTIAL
EQUATION 290 12.2 LINEAR QUADRATIC CONTROL PROBLEM 291 EXERCISES 297
SOLUTIONS TO EXERCISES 297 13. WAVELETS 298 13.1 RECAPITULATION OF SOME
BASIC CONCEPTS 298 13.2 CONTINUOUS WAVELET TRANSFORM 300 CONTENTS XVII
13.3 EXAMPLES OF WAVELETS 301 13.4 DECAY OF CONTINUOUS WAVELET TRANSFORM
308 13.5 MULTIRESOLUTION ANALYSIS 310 EXAMPLES OF MULTIRESOLUTION
ANALYSIS 311 IMPORTANT PROPERTIES OF MRA 311 13.6 DECOMPOSITION AND
RECONSTRUCTION ALGORITHMS 319 13.7 BESTAF-TERMAPPROXIMATION 320 13.8
WAVELET AND FUNCTION SPACES 322 EXERCISES 322 APPENDIX A 325 APPENDIX B
328 APPENDIX C 331 APPENDIX D 335 APPENDIX E 343 APPENDIX F 345
REFERENCES 351 INDEX 359 |
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| ctrlnum | (OCoLC)85689430 (DE-599)GBV525505032 |
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| index_date | 2024-07-02T18:52:09Z |
| indexdate | 2024-07-09T21:07:46Z |
| institution | BVB |
| isbn | 1904798918 |
| language | English |
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| physical | XVII, 362 S. graph. Darst. 25 cm |
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| publisher | Anshan [u.a.] |
| record_format | marc |
| spelling | Siddiqi, Abul Hasan Verfasser aut Introduction to functional analysis with applications A. H. Siddiqi, Khalil Ahmad, P. Manchanda Functional analysis with applications Tunbridge Wells [u.a.] Anshan [u.a.] 2006 XVII, 362 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [351] - 358 Functional analysis Functional equations Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Ahmad, Khalil Sonstige oth Manchanda, Pammy Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Siddiqi, Abul Hasan Introduction to functional analysis with applications Functional analysis Functional equations Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4151278-9 |
| title | Introduction to functional analysis with applications |
| title_alt | Functional analysis with applications |
| title_auth | Introduction to functional analysis with applications |
| title_exact_search | Introduction to functional analysis with applications |
| title_exact_search_txtP | Introduction to functional analysis with applications |
| title_full | Introduction to functional analysis with applications A. H. Siddiqi, Khalil Ahmad, P. Manchanda |
| title_fullStr | Introduction to functional analysis with applications A. H. Siddiqi, Khalil Ahmad, P. Manchanda |
| title_full_unstemmed | Introduction to functional analysis with applications A. H. Siddiqi, Khalil Ahmad, P. Manchanda |
| title_short | Introduction to functional analysis with applications |
| title_sort | introduction to functional analysis with applications |
| topic | Functional analysis Functional equations Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Functional equations Funktionalanalysis Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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