Frames for undergraduates:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2007
|
| Schriftenreihe: | Student mathematical library
40 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIV, 295 S. Ill., graph. Darst. |
| ISBN: | 9780821842126 |
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Datensatz im Suchindex
| _version_ | 1804137342417502208 |
|---|---|
| adam_text | DEGUANG HAN KERI KORNELSON DAVID LARSON ERIC WEBER -AM, AMERICAN
MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS PREFACE FOR
INSTRUCTORS IX ACKNOWLEDGEMENTS XIII INTRODUCTION 1 CHAPTER 1. LINEAR
ALGEBRA REVIEW 5 §1.1. VECTOR SPACES 5 §1.2. BASES FOR VECTOR SPACES 8
§1.3. LINEAR OPERATORS AND MATRICES 17 §1.4. THE RANK OF A LINEAR
OPERATOR AND A MATRIX 23 §1.5. DETERMINANT AND TRACE 25 §1.6. INNER
PRODUCTS AND ORTHONORMAL BASES 27 §1.7. ORTHOGONAL DIRECT SUM 34 §1.8.
EXERCISES FROM THE TEXT 36 §1.9. ADDITIONAL EXERCISES 37 CHAPTER 2.
FINITE-DIMENSIONAL OPERATOR THEORY 41 §2.1. LINEAR FUNCTIONALS AND THE
DUAL SPACE 41 §2.2. RIESZ REPRESENTATION THEOREM AND ADJOINT OPERATORS
43 §2.3. SELF-ADJOINT AND UNITARY OPERATORS 46 §2.4. ORTHOGONAL
COMPLEMENTS AND PROJECTIONS 52 VI CONTENTS §2.5. THE MOORE-PENROSE
INVERSE §2.6. EIGENVALUES FOR OPERATORS §2.7. SQUARE ROOTS OF POSITIVE
OPERATORS §2.8. THE POLAR DECOMPOSITION §2.9. TRACES OF OPERATORS §2.10.
THE OPERATOR NORM §2.11. THE SPECTRAL THEOREM §2.12. EXERCISES FROM THE
TEXT §2.13. ADDITIONAL EXERCISES CHAPTER 3. INTRODUCTION TO FINITE
FRAMES §3.1. R N -FRAMES §3.2. PARSEVAL FRAMES §3.3. GENERAL FRAMES AND
THE CANONICAL RECONSTRUCTION FORMULA §3.4. FRAMES AND MATRICES §3.5.
SIMILARITY AND UNITARY EQUIVALENCE OF FRAMES §3.6. FRAME POTENTIAL §3.7.
NUMERICAL ALGORITHMS §3.8. EXERCISES FROM THE TEXT §3.9. ADDITIONAL
EXERCISES CHAPTER 4. FRAMES IN M. 2 §4.1. DIAGRAM VECTORS §4.2.
EQUIVALENCE OF FRAMES §4.3. UNIT TIGHT FRAMES WITH FOUR VECTORS §4.4.
UNIT TIGHT FRAMES WITH K VECTORS §4.5. FRAME SURGERY: REMOVALS AND
REPLACEMENTS §4.6. FUNDAMENTAL INEQUALITY IN R 2 §4.7. EXERCISES FROM
THE TEXT §4.8. ADDITIONAL EXERCISES CHAPTER 5. THE DILATION PROPERTY OF
FRAMES CONTENTS VII §5.1. ORTHOGONAL COMPRESSIONS OF BASES 141 §5.2.
DILATIONS OF FRAMES 144 §5.3. FRAMES AND OBLIQUE PROJECTIONS 149 §5.4.
EXERCISES FROM THE TEXT 152 §5.5. ADDITIONAL EXERCISES 152 CHAPTER 6.
DUAL AND ORTHOGONAL FRAMES 155 §6.1. RECONSTRUCTION FORMULA REVISITED
155 §6.2. DUAL FRAMES 156 §6.3. ORTHOGONALITY OF FRAMES 163 §6.4.
DISJOINT FRAMES 168 §6.5. SUPER-FRAMES AND MULTIPLEXING 172 §6.6.
PARSEVAL DUAL FRAMES 174 §6.7. EXERCISES FROM THE TEXT 179 §6.8.
ADDITIONAL EXERCISES 180 CHAPTER 7. FRAME OPERATOR DECOMPOSITIONS 183
§7.1. CONTINUITY OF EIGENVALUES 184 §7.2. ELLIPSOIDAL TIGHT FRAMES 189
§7.3. FRAMES WITH A SPECIFIED FRAME OPERATOR 196 §7.4. EXERCISES 203
CHAPTER 8. HARMONIC AND GROUP FRAMES 205 . §8.1. HARMONIC FRAMES 205
§8.2. FRAME REPRESENTATIONS AND GROUP FRAMES 213 §8.3. FRAME VECTORS FOR
UNITARY SYSTEMS 220 §8.4. EXERCISES 226 CHAPTER 9. SAMPLING THEORY 229
§9.1. AN INSTRUCTIVE EXAMPLE 229 §9.2. SAMPLING OF POLYNOMIALS 231 §9.3.
SAMPLING IN FINITE-DIMENSIONAL SPACES 236 §9.4. AN APPLICATION: IMAGE
RECONSTRUCTION 246 VIII CONTENTS §9.5. SAMPLING IN INFINITE-DIMENSIONAL
SPACES 253 §9.6. EXERCISES 263 CHAPTER 10. STUDENT PRESENTATIONS 265
§10.1. EIGENSPACE DECOMPOSITION 265 §10.2. SQUARE ROOTS OF POSITIVE
OPERATORS 268 §10.3. POLAR DECOMPOSITION 270 §10.4. OBLIQUE PROJECTIONS
AND FRAMES 274 §10.5. VANDERMONDE DETERMINANT 277 CHAPTER 11. ANECDOTES:
FRAME THEORY PROJECTS BY UNDERGRADUATES 281 BIBLIOGRAPHY 287 INDEX OF
SYMBOLS 291 INDEX 293
|
| adam_txt |
DEGUANG HAN KERI KORNELSON DAVID LARSON ERIC WEBER -AM, AMERICAN
MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS PREFACE FOR
INSTRUCTORS IX ACKNOWLEDGEMENTS XIII INTRODUCTION 1 CHAPTER 1. LINEAR
ALGEBRA REVIEW 5 §1.1. VECTOR SPACES 5 §1.2. BASES FOR VECTOR SPACES 8
§1.3. LINEAR OPERATORS AND MATRICES 17 §1.4. THE RANK OF A LINEAR
OPERATOR AND A MATRIX 23 §1.5. DETERMINANT AND TRACE 25 §1.6. INNER
PRODUCTS AND ORTHONORMAL BASES 27 §1.7. ORTHOGONAL DIRECT SUM 34 §1.8.
EXERCISES FROM THE TEXT 36 §1.9. ADDITIONAL EXERCISES 37 CHAPTER 2.
FINITE-DIMENSIONAL OPERATOR THEORY 41 §2.1. LINEAR FUNCTIONALS AND THE
DUAL SPACE 41 §2.2. RIESZ REPRESENTATION THEOREM AND ADJOINT OPERATORS
43 §2.3. SELF-ADJOINT AND UNITARY OPERATORS 46 §2.4. ORTHOGONAL
COMPLEMENTS AND PROJECTIONS 52 VI CONTENTS §2.5. THE MOORE-PENROSE
INVERSE §2.6. EIGENVALUES FOR OPERATORS §2.7. SQUARE ROOTS OF POSITIVE
OPERATORS §2.8. THE POLAR DECOMPOSITION §2.9. TRACES OF OPERATORS §2.10.
THE OPERATOR NORM §2.11. THE SPECTRAL THEOREM §2.12. EXERCISES FROM THE
TEXT §2.13. ADDITIONAL EXERCISES CHAPTER 3. INTRODUCTION TO FINITE
FRAMES §3.1. R N -FRAMES §3.2. PARSEVAL FRAMES §3.3. GENERAL FRAMES AND
THE CANONICAL RECONSTRUCTION FORMULA §3.4. FRAMES AND MATRICES §3.5.
SIMILARITY AND UNITARY EQUIVALENCE OF FRAMES §3.6. FRAME POTENTIAL §3.7.
NUMERICAL ALGORITHMS §3.8. EXERCISES FROM THE TEXT §3.9. ADDITIONAL
EXERCISES CHAPTER 4. FRAMES IN M. 2 §4.1. DIAGRAM VECTORS §4.2.
EQUIVALENCE OF FRAMES §4.3. UNIT TIGHT FRAMES WITH FOUR VECTORS §4.4.
UNIT TIGHT FRAMES WITH K VECTORS §4.5. FRAME SURGERY: REMOVALS AND
REPLACEMENTS §4.6. FUNDAMENTAL INEQUALITY IN R 2 §4.7. EXERCISES FROM
THE TEXT §4.8. ADDITIONAL EXERCISES CHAPTER 5. THE DILATION PROPERTY OF
FRAMES CONTENTS VII §5.1. ORTHOGONAL COMPRESSIONS OF BASES 141 §5.2.
DILATIONS OF FRAMES 144 §5.3. FRAMES AND OBLIQUE PROJECTIONS 149 §5.4.
EXERCISES FROM THE TEXT 152 §5.5. ADDITIONAL EXERCISES 152 CHAPTER 6.
DUAL AND ORTHOGONAL FRAMES 155 §6.1. RECONSTRUCTION FORMULA REVISITED
155 §6.2. DUAL FRAMES 156 §6.3. ORTHOGONALITY OF FRAMES 163 §6.4.
DISJOINT FRAMES 168 §6.5. SUPER-FRAMES AND MULTIPLEXING 172 §6.6.
PARSEVAL DUAL FRAMES 174 §6.7. EXERCISES FROM THE TEXT 179 §6.8.
ADDITIONAL EXERCISES 180 CHAPTER 7. FRAME OPERATOR DECOMPOSITIONS 183
§7.1. CONTINUITY OF EIGENVALUES 184 §7.2. ELLIPSOIDAL TIGHT FRAMES 189
§7.3. FRAMES WITH A SPECIFIED FRAME OPERATOR 196 §7.4. EXERCISES 203
CHAPTER 8. HARMONIC AND GROUP FRAMES 205 . §8.1. HARMONIC FRAMES 205
§8.2. FRAME REPRESENTATIONS AND GROUP FRAMES 213 §8.3. FRAME VECTORS FOR
UNITARY SYSTEMS 220 §8.4. EXERCISES 226 CHAPTER 9. SAMPLING THEORY 229
§9.1. AN INSTRUCTIVE EXAMPLE 229 §9.2. SAMPLING OF POLYNOMIALS 231 §9.3.
SAMPLING IN FINITE-DIMENSIONAL SPACES 236 §9.4. AN APPLICATION: IMAGE
RECONSTRUCTION 246 VIII CONTENTS §9.5. SAMPLING IN INFINITE-DIMENSIONAL
SPACES 253 §9.6. EXERCISES 263 CHAPTER 10. STUDENT PRESENTATIONS 265
§10.1. EIGENSPACE DECOMPOSITION 265 §10.2. SQUARE ROOTS OF POSITIVE
OPERATORS 268 §10.3. POLAR DECOMPOSITION 270 §10.4. OBLIQUE PROJECTIONS
AND FRAMES 274 §10.5. VANDERMONDE DETERMINANT 277 CHAPTER 11. ANECDOTES:
FRAME THEORY PROJECTS BY UNDERGRADUATES 281 BIBLIOGRAPHY 287 INDEX OF
SYMBOLS 291 INDEX 293 |
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| id | DE-604.BV023090028 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:40:36Z |
| indexdate | 2024-07-09T21:10:46Z |
| institution | BVB |
| isbn | 9780821842126 |
| language | English |
| lccn | 2007060796 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016292910 |
| oclc_num | 156975410 |
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| owner | DE-20 DE-634 DE-703 DE-83 DE-188 |
| owner_facet | DE-20 DE-634 DE-703 DE-83 DE-188 |
| physical | XIV, 295 S. Ill., graph. Darst. |
| publishDate | 2007 |
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| publisher | American Math. Soc. |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spelling | Frames for undergraduates Deguang Han ... Providence, RI American Math. Soc. 2007 XIV, 295 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Student mathematical library 40 Includes bibliographical references and index Frames (Vector analysis) Frame Mathematik (DE-588)4528312-6 gnd rswk-swf Frame Mathematik (DE-588)4528312-6 s DE-604 Han, Deguang Sonstige oth Erscheint auch als Online-Ausgabe 978-1-4704-2149-6 Student mathematical library 40 (DE-604)BV013184751 40 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016292910&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frames for undergraduates Student mathematical library Frames (Vector analysis) Frame Mathematik (DE-588)4528312-6 gnd |
| subject_GND | (DE-588)4528312-6 |
| title | Frames for undergraduates |
| title_auth | Frames for undergraduates |
| title_exact_search | Frames for undergraduates |
| title_exact_search_txtP | Frames for undergraduates |
| title_full | Frames for undergraduates Deguang Han ... |
| title_fullStr | Frames for undergraduates Deguang Han ... |
| title_full_unstemmed | Frames for undergraduates Deguang Han ... |
| title_short | Frames for undergraduates |
| title_sort | frames for undergraduates |
| topic | Frames (Vector analysis) Frame Mathematik (DE-588)4528312-6 gnd |
| topic_facet | Frames (Vector analysis) Frame Mathematik |
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