An operator perspective on signals and systems:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2010
|
| Series: | Operator Theory
204 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 429 S. graph. Darst. |
| ISBN: | 9783034602914 |
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MARC
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Record in the Search Index
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| adam_text | CONTENTS PREFACE BASIC OPERATOR THEORY 1 THE WOLD DECOMPOSITION 3 1.1
THE UNILATERAL SHIFT 3 1.2 THE EIGENVALUES FOR THE BACKWARD SHIFT 6 1.3
THE WOLD DECOMPOSITION 8 1.4 THE BILATERAL SHIFT 11 1.5 ABSTRACT
TOEPLITZ OPERATORS 16 1.5.1 ABSTRACT TOEPLITZ OPERATORS VIEWED AS A
COMPRESSION .... 19 1.6 NOTES 22 TOEPLITZ AND LAURENT OPERATORS 23 2.1
THE FOURIER TRANSFORM 23 2.1.1 THE SUBSPACE L {) 24 2.2 HARDY SPACES 25
2.3 MULTIPLICATION OPERATORS 29 2.4 LAURENT OPERATORS 31 2.5 TOEPLITZ
OPERATORS AND MATRICES 34 2.6 TOEPLITZ MATRICES AND H FUNCTIONS 36 2.7
NOTES 40 INNER AND OUTER FUNCTIONS 41 3.1 THE BEURLING-LAX-HALMOS
THEOREM 41 3.1.1 THE INVARIANT SUBSPACES FOR THE BACKWARD SHIFT 43 3.2
INNER-OUTER FACTORIZATIONS 45 3.3 INVERTIBLE OUTER FUNCTIONS 49 3.4 THE
DETERMINANT OF INNER AND OUTER FUNCTIONS 51 3.5 NOTES 53 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/996813675 DIGITALISIERT DURCH II CONTENTS
RATIONAL INNER AND OUTER FUNCTIONS 55 4.1 BLASCHKE PRODUCTS 55 4.2 STATE
SPACE REALIZATIONS FOR RATIONAL INNER FUNCTIONS 58 4.3 RATIONAL
TWO-SIDED INNER FUNCTIONS 64 4.4 RATIONAL OUTER FUNCTIONS 68 4.5
INNER-OUTER FACTORIZATION AND MCMILLAN DEGREE 72 4.6 INNER-OUTER
FACTORIZATION AND FINITE SECTIONS 78 4.7 THE DOUGLAS-SHAPIRO-SHIELDS
FACTORIZATION 81 4.8 THE DOUGLAS-SHAPIRO-SHIELDS FACTORIZATION FOR
RATIONAL FUNCTIONS 85 4.8.1 A FACTORIZATION FOR RATIONAL L FUNCTIONS
86 4.9 NOTES 88 THE NAIMARK REPRESENTATION 91 5.1 THE NAIMARK
REPRESENTATION THEOREM 92 5.2 THE MAXIMAL OUTER SPECTRAL FACTOR 97 5.2.1
THE EIGENSPACE FOR THE UNITARY PART 102 5.3 THE INNER-OUTER
FACTORIZATION REVISITED 103 5.4 POSITIVE REAL FUNCTIONS 106 5.5 MINIMAL
ISOMETRIC LIFTINGS 110 5.6 NOTES 113 THE RATIONAL CASE 117 6.1 RATIONAL
SYMBOLS 117 6.2 THE POSITIVE REAL LEMMA 123 6.3 FINITE DIMENSIONAL
UNITARY PART 125 6.4 A CLASSICAL ERGODIC RESULT 127 6.5 ANOTHER ERGODIC
RESULT 130 6.6 NOTES 135 II FINITE SECTION TECHNIQUES 143 7 THE LEVINSON
ALGORITHM AND FACTORIZATION 145 7.1 THE CASE WHEN T R IS INVERTIBLE 145
7. CONTENTS IX 7.9 A SPECTRAL FACTORIZATION APPROACH TO FILTERING 171
7.10 NOTES 175 8 ISOMETRIC REPRESENTATIONS AND FACTORIZATION 179 8.1
ISOMETRIC REPRESENTATIONS AND FINITE SECTIONS 179 8.2 A BASIC
OPTIMIZATION PROBLEM 185 8.3 THE LOWER TRIANGULAR CHOLESKY FACTORIZATION
188 8.4 CHOLESKY FACTORIZATION AND MAXIMAL OUTER SPECTRAL FACTORS 194
8.5 SOME EXAMPLES OF THE CHOLESKY FACTORIZATION 197 8.5.1 SCALAR-VALUED
OUTER FUNCTION 197 8.5.2 MULTI-INPUT MULTI-OUTPUT SQUARE OUTER FUNCTION
198 8.5.3 NON-SQUARE OUTER FUNCTION 199 8.5.4 NON-SQUARE OUTER FUNCTION
AND A UNITARY PART 201 8.6 AN INNER-OUTER FACTORIZATION ALGORITHM 202
8.6.1 A SCALAR INNER-OUTER FACTORIZATION EXAMPLE 203 8.6.2 A NON-SQUARE
INNER-OUTER FACTORIZATION EXAMPLE 204 8.6.3 AN OUTER FUNCTION AND A
UNITARY PART 205 8.7 NOTES 206 9 SIGNAL PROCESSING 209 9.1 A FUNDAMENTAL
OPTIMIZATION PROBLEM 209 9.2 SINUSOID ESTIMATION 213 9.3 SINUSOID
ESTIMATION: CAPON-GERONIMUS 221 9.4 A NESTED OPTIMIZATION PROBLEM 223
9.5 LIMIT THEOREMS 226 9.6 THE OUTER FUNCTION K N (Z,A) 233 9.7 NOTES
239 III RICCATI METHODS 245 10 RICCATI EQUATIONS AND FACTORIZATION 247
10.1 ALGEBRAIC RICCATI EQUATIONS 247 10. X CONTENTS 11 KALMAN AND WIENER
FILTERING 283 11.1 RANDOM VECTORS 284 11.2 LEAST SQUARES ESTIMATION OF A
RANDOM VECTOR 285 11.3 TIME VARYING STATE SPACE SYSTEMS 288 11.4 THE
KALMAN FILTER 289 11.5 THE STEADY STATE KALMAN FILTER 294 11.6 WIDE
SENSE STATIONARY PROCESSES 295 11.6.1 A SINUSOID PROCESS 297 11.7 THE
SPECTRAL DENSITY 299 11.8 JOINTLY WIDE SENSE STATIONARY PROCESSES 300
11.9 WIENER FILTERING 302 11.10 STEADY STATE KALMAN AND WIENER FILTERING
305 11.10.1 STATE SPACE SYSTEMS WITH X(* OO) = 0 305 11.10.2 THE WIENER
FILTER FOR {A, B, C, D} 309 11.11 NOTES 312 IV INTERPOLATION THEORY 315
12 TANGENTIAL NEVANLINNA-PICK INTERPOLATION 317 12.1 AN INTRODUCTION TO
NEVANLINNA-PICK INTERPOLATION 317 12.2 THE FIRST MAIN RESULT ON
INTERPOLATION 321 12.3 PROOF OF THEOREM 12.1.1 328 12.4 PROOF OF THEOREM
12.1.3 330 12.5 THE CASE WHEN A IS STRICTLY POSITIVE 332 12.6 THE
CARATHEODORY INTERPOLATION PROBLEM 337 12.7 NOTES 339 13 CONTRACTIVE
NEVANLINNA-PICK INTERPOLATION 341 13.1 ISOMETRIC REALIZATIONS 341 13.1.1
RATIONAL CONTRACTIVE REALIZATIONS 353 13.2 TANGENTIAL NEVANLINNA-PICK
INTERPOLATION 356 13.3 ISOMETRIC REALIZATIONS REVISITED 365 13.4 THE
MAXIMUM PRINCIPLE 366 13. CONTENTS XI 14.4 THE CONTROLLABILITY AND
OBSERVABILITY GRAMIAN 386 14.5 THE KALMAN-HO ALGORITHM 388 14.6 THE
RESTRICTED BACKWARD SHIFT REALIZATION 393 14.6.1 RATIONAL FUNCTIONS IN H
2 (, Y) 395 14.6.2 THE RESTRICTED BACKWARD SHIFT REALIZATION IN H 2 396
14.7 NOTES 397 15 THE LEVINSON ALGORITHM 399 15.1 THE LEVINSON RECURSION
399 15.2 THE SCALAR CASE 404 15.3 THE GOHBERG-SEMENCUL-HEINIG INVERSION
FORMULA 407 15.4 NOTES 411 BIBLIOGRAPHY 413 INDEX 427
|
| any_adam_object | 1 |
| author | Frazho, Arthur E. Bhosri, Wisuwat |
| author_facet | Frazho, Arthur E. Bhosri, Wisuwat |
| author_role | aut aut |
| author_sort | Frazho, Arthur E. |
| author_variant | a e f ae aef w b wb |
| building | Verbundindex |
| bvnumber | BV025585062 |
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| dewey-full | 515.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.724 |
| dewey-search | 515.724 |
| dewey-sort | 3515.724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV025585062 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:36:58Z |
| institution | BVB |
| isbn | 9783034602914 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020182026 |
| oclc_num | 465370463 |
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| owner | DE-11 DE-83 DE-824 |
| owner_facet | DE-11 DE-83 DE-824 |
| physical | XI, 429 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator Theory |
| series2 | Operator theory |
| spelling | Frazho, Arthur E. Verfasser aut An operator perspective on signals and systems Arthur E. Frazho ; Wisuwat Bhosri Basel [u.a.] Birkhäuser 2010 XI, 429 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Operator theory 204 : Linear operators and linear systems Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Zustandsraum (DE-588)4132647-7 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Faktorisierung (DE-588)4128927-4 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s Faktorisierung (DE-588)4128927-4 s Interpolation (DE-588)4162121-9 s Zustandsraum (DE-588)4132647-7 s Signalverarbeitung (DE-588)4054947-1 s DE-604 Bhosri, Wisuwat Verfasser aut Erscheint auch als Online-Ausgabe 978-3-0346-0292-1 Operator Theory Advances and Applications /Linear Operators and Linear Systems 204 (DE-604)BV000000970 204 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020182026&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frazho, Arthur E. Bhosri, Wisuwat An operator perspective on signals and systems Operator Theory Signalverarbeitung (DE-588)4054947-1 gnd Zustandsraum (DE-588)4132647-7 gnd Interpolation (DE-588)4162121-9 gnd Operatortheorie (DE-588)4075665-8 gnd Faktorisierung (DE-588)4128927-4 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4132647-7 (DE-588)4162121-9 (DE-588)4075665-8 (DE-588)4128927-4 |
| title | An operator perspective on signals and systems |
| title_auth | An operator perspective on signals and systems |
| title_exact_search | An operator perspective on signals and systems |
| title_full | An operator perspective on signals and systems Arthur E. Frazho ; Wisuwat Bhosri |
| title_fullStr | An operator perspective on signals and systems Arthur E. Frazho ; Wisuwat Bhosri |
| title_full_unstemmed | An operator perspective on signals and systems Arthur E. Frazho ; Wisuwat Bhosri |
| title_short | An operator perspective on signals and systems |
| title_sort | an operator perspective on signals and systems |
| topic | Signalverarbeitung (DE-588)4054947-1 gnd Zustandsraum (DE-588)4132647-7 gnd Interpolation (DE-588)4162121-9 gnd Operatortheorie (DE-588)4075665-8 gnd Faktorisierung (DE-588)4128927-4 gnd |
| topic_facet | Signalverarbeitung Zustandsraum Interpolation Operatortheorie Faktorisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020182026&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT frazhoarthure anoperatorperspectiveonsignalsandsystems AT bhosriwisuwat anoperatorperspectiveonsignalsandsystems |