Applied functional analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, FL [u.a.]
CRC Press
2010
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVII, 578 S. graph. Darst. |
| ISBN: | 9781420091953 |
Internformat
MARC
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| 245 | 1 | 0 | |a Applied functional analysis |c J. Tinsley Oden ; Leszek F. Demkowicz |
| 250 | |a 2. ed. | ||
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| 300 | |a XVII, 578 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804143086788411392 |
|---|---|
| adam_text | APPLIED FUNCTIONAL ANALYSIS LESZELC F. DEMKOWICZ INSTITUTE FOR
COMPUTATIONAL ENGINEERING AND SCIENCES (ICES) THE UNIVERSITY OF TEXAS AT
AUSTIN TECHNISCHE INFORMATIONSBIBLIOTHEK UNIVERSITATSBIBLIOTHEK HANNOVER
SECOND EDITION TAYLOR& FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC
PRESS IS AN IMPRINT OF THE TAYLOR 6C FRANCIS GROUP, AN INFORMA BUSINESS
CONTENTS 1 PRELIMINARIES 1 ELEMENTARYLOGIC AND SET THEORY 1.1 SETS AND
PRELIMINARYNOTATIONS, NUMBER SETS 1 1.2 LEVEL ONE LOGIC 3 1.3 ALGEBRA OF
SETS 9 1.4 LEVEL TWO LOGIC 16 1.5 INFINITE UNIONS AND INTERSECTIONS 18
RELATIONS 1.6 CARTESIAN PRODUCTS, RELATIONS 21 1.7 PARTIALORDERINGS 26
1.8 EQUIVALENCE RELATIONS, EQUIVALENCE CLASSES, PARTITIONS 31 FUNCTIONS
1.9 FUNDAMENTAL DEFINITIONS 36 1.10 COMPOSITIONS, INVERSE FUNCTIONS 43
CARDINALITYOF SETS 1.11 FUNDAMENTAL NOTIONS 52 1.12 ORDERINGOF
CARDINALNUMBERS 54 FOUNDATIONS OF ABSTRACT ALGEBRA 1.13 OPERATIONS,
ABSTRACTSYSTEMS, ISOMORPHISMS 58 1.14 EXAMPLES OFABSTRACTSYSTEMS 63
ELEMENTARY TOPOLOGYINIE 1.15 THEREALNUMBERSYSTEM 73 1.16 OPEN AND
CLOSED SETS 78 1.17 SEQUENCES 85 1.18 LIMITS AND CONTINUITY * 92 XIII
XIV ELEMENTS OF DIFFERENTIAL AND INTEGRAL CALCULUS 1.19 DERIVATIVES AND
INTEGRALS OF FUNCTIONS OFONE VARIABLE 97 1.20 MULTIDIMENSIONAL CALCULUS
104 2 LINEAR ALGEBRA 111 VECTOR SPACES*THE BASIC CONCEPTS 2.1 CONCEPTOF
A VECTOR SPACE ILL 2.2 SUBSPACES 118 2.3 EQUIVALENCE RELATIONS AND
QUOTIENTSPACES 123 2.4 LINEARDEPENDENCE ANDINDEPENDENCE, HAMEL BASIS,
DIMENSION 129 LINEARTRANSFORMATIONS 2.5 LINEARTRANSFORMATIONS*THE
FUNDAMENTAL FACTS 139 2.6 ISOMORPHIC VECTORSPACES 146 2.7
MOREABOUTLINEAR TRANSFORMATIONS 150 2.8 LINEARTRANSFORMATIONS AND
MATRICES 156 2.9 SOLVABILITY OF LINEAR EQUATIONS 159 ALGEBRAICDUALS 2.10
THE ALGEBRAIC DUAL SPACE, DUAL BASIS 162 2.11 TRANSPOSE OFA LINEAR
TRANSFORMATION 170 2.12 TENSOR PRODUCTS, COVARIANT AND CONTRAVARIANT
TENSORS 176 2.13 ELEMENTS OF MULTILINEARALGEBRA 181 EUCLIDEANSPACES 2.14
SCALAR (INNER) PRODUCT, REPRESENTATION THEOREM IN
FINITE-DIMENSIONALSPACES 188 2.15 BASIS ANDCOBASIS, ADJOINT
OFATRANSFORMATION,CONTRA- ANDCOVARIANT COMPONENTS OFTEN SORS 192 3
LEBESGUEMEASURE AND INTEGRATION 201 LEBESGUEMEASURE 3.1 ELEMENTARY
ABSTRACTMEASURE THEORY 201 3.2 CONSTRUCTIONOFLEBESGUEMEASURE INRN 210
3.3 THE FUNDAMENTAL CHARACTERIZATION OFLEBESGUEMEASURE 221 LEBESGUE
INTEGRATION THEORY XV 3.4 MEASURABLE AND BOREL FUNCTIONS 230 3.5
LEBESGUE INTEGRAL OFNONNEGATIVEFUNCTIONS 233 3.6 FUBINI S THEOREM FOR
NONNEGATIVE FUNCTIONS 238 3.7 LEBESGUE INTEGRAL OF ARBITRARYFUNCTIONS
245 3.8 LEBESGUE APPROXIMATION SUMS, RIEMANN INTEGRALS 254 IP SPACES 3.9
HOLDERAND MINKOWSKI INEQUALITIES 260 4 TOPOLOGICAL ANDMETRICSPACES 269
ELEMENTARY TOPOLOGY 4.1 TOPOLOGICALSTRUCTURE*BASIC NOTIONS 269 4.2
TOPOLOGICALSUBSPACES AND PRODUCTTOPOLOGIES 287 4.3 CONTINUITY
ANDCOMPACTNESS 291 4.4 SEQUENCES 301 4.5 TOPOLOGICAL EQUIVALENCE.
HOMEOMORPHISM 306 THEORY OFMETRIC SPACES 4.6 METRIC AND NORMED SPACES,
EXAMPLES 308 4.7 TOPOLOGICAL PROPERTIES OFMETRIC SPACES 316 4.8
COMPLETENESS AND COMPLETION OFMETRIC SPACES 321 4.9 COMPACTNESS IN
METRIC SPACES 333 4.10 CONTRACTION MAPPINGS AND FIXED POINTS 346 5
BANACH SPACES 355 TOPOLOGICAL VECTORSPACES 5.1 TOPOLOGICAL VECTOR
SPACES*AN INTRODUCTION 355 5.2 LOCALLY CONVEXTOPOLOGICAL VECTOR SPACES
357 5.3 SPACE OF TEST FUNCTIONS 364 HAHN-BANACH EXTENSION THEOREM 5.4
THE HAHN-BANACH THEOREM 368 5.5 EXTENSIONSAND COROLLARIES 371
BOUNDED(CONTINUOUS) LINEAR OPERATORS ON NORMED SPACES 5.6 FUNDAMENTAL
PROPERTIES OFLINEAR BOUNDED OPERATORS 374 XVI 5.7 THE SPACE OFCONTINUOUS
LINEAR OPERATORS 382 5.8 UNIFORM BOUNDEDNESS AND BANACH-STEINHAUS
THEOREMS 387 5.9 THE OPEN MAPPING THEOREM 389 CLOSED OPERATORS 5.10
CLOSED OPERATORS, CLOSEDGRAPHTHEOREM 392 5.11 EXAMPLE OF ACLOSED
OPERATOR 398 TOPOLOGICAL DUALS. WEAK COMPACTNESS 5.12 EXAMPLES
OFDUALSPACES, REPRESENTATION THEOREM FOR TOPOLOGICAL DUALS OFLP SPACES .
. 401 5.13 BIDUAL, REFLEXIVE SPACES 412 5.14 WEAK
TOPOLOGIES,WEAKSEQUENTIAL COMPACTNESS 417 5.15 COMPACT(COMPLETELY
CONTINUOUS) OPERATORS 425 CLOSEDRANGETHEOREM. SOLVABILITY OFLINEAR
EQUATIONS 5.16 TOPOLOGICAL TRANSPOSE OPERATORS, ORTHOGONAL COMPLEMENTS
430 5.17 SOLVABILITY OFLINEAR EQUATIONS IN BANACH SPACES, THE
CLOSEDRANGE THEOREM 434 5.18 GENERALIZATION FORCLOSED OPERATORS 439 5.19
EXAMPLES 443 5.20 EQUATIONS WITH COMPLETELY CONTINUOUS KERNELS. FREDHOLM
ALTERNATIVE 449 6 HILBERT SPACES 463 BASIC THEORY 6.1 INNERPRODUCTAND
HILBERT SPACES 463 6.2 ORTHOGONALITY ANDORTHOGONAL PROJECTIONS 480 6.3
ORTHONORMAL BASES ANDFOURIER SERIES 487 DUALITY IN HILBERTSPACES 6.4
RIESZREPRESENTATIONTHEOREM 498 6.5 THE ADJOINT OF A LINEAROPERATOR 506
6.6 VARIATIONAL BOUNDARY-VALUE PROBLEMS , 516 6.7
GENERALIZEDGREEN SFORMULAS FOR OPERATORS ON HILBERT SPACES 530 ELEMENTS
OF SPECTRAL THEORY 6.8 RESOLVENT SETANDSPECTRUM 540 6.9 SPECTRA
OFCONTINUOUS OPERATORS. FUNDAMENTALPROPERTIES 545 XVII 6.10 SPECTRAL
THEORY FOR COMPACTOPERATORS 550 6.11 SPECTRAL THEORY FOR SELF-ADJOINT
OPERATORS 560 7 REFERENCES 569 INDEX 570
|
| any_adam_object | 1 |
| author | Oden, John Tinsley 1936-2023 Demkowicz, Leszek |
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| 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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| indexdate | 2024-07-09T22:42:04Z |
| institution | BVB |
| isbn | 9781420091953 |
| language | English |
| lccn | 2009047507 |
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| physical | XVII, 578 S. graph. Darst. |
| publishDate | 2010 |
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| spelling | Oden, John Tinsley 1936-2023 Verfasser (DE-588)108393224 aut Applied functional analysis J. Tinsley Oden ; Leszek F. Demkowicz 2. ed. Boca Raton, FL [u.a.] CRC Press 2010 XVII, 578 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Demkowicz, Leszek Verfasser (DE-588)136188044 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020438669&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 |
| spellingShingle | Oden, John Tinsley 1936-2023 Demkowicz, Leszek Applied functional analysis Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4123623-3 |
| title | Applied functional analysis |
| title_auth | Applied functional analysis |
| title_exact_search | Applied functional analysis |
| title_full | Applied functional analysis J. Tinsley Oden ; Leszek F. Demkowicz |
| title_fullStr | Applied functional analysis J. Tinsley Oden ; Leszek F. Demkowicz |
| title_full_unstemmed | Applied functional analysis J. Tinsley Oden ; Leszek F. Demkowicz |
| title_short | Applied functional analysis |
| title_sort | applied functional analysis |
| topic | Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Funktionalanalysis Lehrbuch |
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