Limit operators and their applications in operator theory:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Basel
Birkhäuser
2004
|
| Series: | Operator theory
150 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 392 S. |
| ISBN: | 3764370815 |
Staff View
MARC
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| 245 | 1 | 0 | |a Limit operators and their applications in operator theory |c Vladimir Rabinovich ; Steffen Roch ; Bernd Silbermann |
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Record in the Search Index
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| adam_text | LIT OPERATORS AND THEIR APPLICATIONS IN OPERATOR THEORY VLADIMIR
RABINOVICH STEFFEN ROCH BERND SILBERMANN BIRKHAUSER VERLAG BASEL *
BOSTON * BERLIN CONTENTS PREFACE XI 1 LIMIT OPERATORS 1.1 GENERALIZED
COMPACTNESS, GENERALIZED CONVERGENCE 1 1.1.1 COMPACTNESS, STRONG
CONVERGENCE, FREDHOLMNESS 1 1.1.2 P-COMPACTNESS 4 1.1.3 P-FREDHOLMNESS
10 1.1.4 P-STRONG CONVERGENCE 11 1.1.5 INVERTIBILITY OF P-STRONG LIMITS
15 1.2 LIMIT OPERATORS 17 1.2.1 LIMIT OPERATORS AND THE OPERATOR
SPECTRUM 17 1.2.2 OPERATORS WITH RICH OPERATOR SPECTRUM 19 1.3
ALGEBRAIZATION 23 1.3.1 ALGEBRAIZATION BY RESTRICTION 24 1.3.2 SYMBOL
CALCULUS 25 1.4 COMMENTS AND REFERENCES 29 2 FREDHOLMNESS OF
BAND-DOMINATED OPERATORS 2.1 BAND-DOMINATED OPERATORS 31 2.1.1 FUNCTION
SPACES ON Z N 31 2.1.2 MATRIX REPRESENTATION 32 2.1.3 OPERATORS OF
MULTIPLICATION 33 2.1.4 BAND AND BAND-DOMINATED OPERATORS 35 2.1.5 LIMIT
OPERATORS OF BAND-DOMINATED OPERATORS 40 2.1.6 RICH BAND-DOMINATED
OPERATORS 43 2.2 V- FREDHOLMNESS OF RICH BAND-DOMINATED OPERATORS 45
2.2.1 THE MAIN THEOREM ON V- FREDHOLMNESS 45 2.2.2 WEAKLY SUFFICIENT
FAMILIES OF HOMOMORPHISMS 51 2.2.3 SYMBOL CALCULUS FOR RICH
BAND-DOMINATED OPERATORS 53 2.2.4 APPENDIX A: SECOND VERSION OF A SYMBOL
CALCULUS 56 2.2.5 APPENDIX B: COMMUTATIVE BANACH ALGEBRAS 59 CONTENTS
2.3 LOCAL P-FREDHOLMNESS: ELEMENTARY THEORY 61 2.3.1 LOCAL OPERATOR
SPECTRA AND LOCAL INVERTIBILITY 61 2.3.2 P7-COMPACTNESS,
P7-FREDHOLMNESS 62 2.3.3 LOCAL P-FREDHOLMNESS OF BAND-DOMINATED
OPERATORS . . . . 64 2.3.4 ALLAN S LOCAL PRINCIPLE 65 2.3.5 LOCAL
P-FREDHOLMNESS OF BAND-DOMINATED OPERATORS IN THE SENSE OF THE LOCAL
PRINCIPLE 69 2.3.6 OPERATORS WITH CONTINUOUS COEFFICIENTS 72 2.4 LOCAL
P-FREDHOLMNESS: ADVANCED THEORY 74 2.4.1 SLOWLY OSCILLATING FUNCTIONS 74
2.4.2 THE MAXIMAL IDEAL SPACE OF SO(Z N ) 79 2.4.3 PRELIMINARIES ON NETS
82 2.4.4 LIMIT OPERATORS WITH RESPECT TO NETS 87 2.4.5 LOCAL
INVERTIBILITY AT POINTS IN M(SO(Z N )) 89 2.4.6 FREDHOLMNESS OF
BAND-DOMINATED OPERATORS WITH SLOWLY OSCILLATING COEFFICIENTS 93 2.4.7
NETS VS. SEQUENCES 94 2.4.8 APPENDIX A: A SECOND PROOF OF THEOREM 2.4.27
95 2.4.9 APPENDIX B: A THIRD PROOF OF THEOREM 2.4.27 100 2.5 OPERATORS
IN THE DISCRETE WIENER ALGEBRA 103 2.5.1 THE WIENER ALGEBRA 103 2.5.2
FREDHOLMNESS OF OPERATORS IN THE WIENER ALGEBRA 107 2.6 BAND-DOMINATED
OPERATORS WITH SPECIAL COEFFICIENTS ILL 2.6.1 BAND-DOMINATED OPERATORS
WITH ALMOST PERIODIC COEFFICIENTS ILL 2.6.2 OPERATORS ON HALF-SPACES 113
2.6.3 OPERATORS ON POLYHEDRAL CONVEX CONES 119 2.6.4 COMPOSED
BAND-DOMINATED OPERATORS ON 1? 124 2.6.5 DIFFERENCE OPERATORS OF SECOND
ORDER 128 2.6.6 DISCRETE SCHRODINGER OPERATORS 131 2.7 INDICES OF
FREDHOLM BAND-DOMINATED OPERATORS 135 2.7.1 MAIN RESULTS 136 2.7.2 THE
ALGEBRA A(Z) AS A CROSSED PRODUCT 138 2.7.3 THE IFI-GROUP OF A(Z) 139
2.7.4 THE I^I-GROUP OF A 142 2.7.5 PROOF OF THEOREM 2.7.1 144 2.7.6
UNITARY BAND-DOMINATED OPERATORS 147 2.8 COMMENTS AND REFERENCES 150
CONVOLUTION TYPE OPERATORS ON R N 3.1 BAND-DOMINATED OPERATORS ON L P (R
N ) 153 3.1.1 APPROXIMATE IDENTITIES AND P-FREDHOLMNESS 153 3.1.2 SHIFTS
AND LIMIT OPERATORS 155 CONTENTS 3.1.3 DISCRETIZATION 155 3.1.4
BAND-DOMINATED OPERATORS ON L P (R N ) 157 3.2 OPERATORS OF CONVOLUTION
159 3.2.1 COMPACTNESS OF SEMI-COMMUTATORS 159 3.2.2 COMPACTNESS OF
COMMUTATORS 164 3.3 FREDHOLMNESS OF CONVOLUTION TYPE OPERATORS 169 3.3.1
OPERATORS OF CONVOLUTION TYPE 169 3.3.2 FREDHOLMNESS 172 3.4
COMPRESSIONS OF CONVOLUTION TYPE OPERATORS 179 3.4.1 COMPRESSIONS OF
OPERATORS IN A{BUC(R N ), C P ) 180 3.4.2 COMPRESSIONS TO A HALF-SPACE
181 3.4.3 COMPRESSIONS TO CURVED HALF-SPACES 182 3.4.4 COMPRESSIONS TO
CURVED LAYERS 184 3.4.5 COMPRESSIONS TO CURVED CYLINDERS 184 3.4.6
COMPRESSIONS TO CONES WITH SMOOTH CROSS SECTION 185 3.4.7 COMPRESSIONS
TO CONES WITH EDGES 190 3.4.8 COMPRESSIONS TO EPIGRAPHS OF FUNCTIONS 193
3.5 A WIENER ALGEBRA OF CONVOLUTION-TYPE OPERATORS 194 3.5.1
FREDHOLMNESS OF OPERATORS IN THE WIENER ALGEBRA 194 3.5.2 THE ESSENTIAL
SPECTRUM OF SCHRODINGER OPERATORS 195 3.6 COMMENTS AND REFERENCES 199
PSEUDODIFFERENTIAL OPERATORS 4.1 GENERALITIES AND NOTATION 201 4.1.1
FUNCTION SPACES AND FOURIER TRANSFORM 201 4.1.2 OSCILLATORY INTEGRALS
203 4.1.3 PSEUDODIFFERENTIAL OPERATORS 204 4.1.4 FORMAL SYMBOLS 205
4.1.5 PSEUDODIFFERENTIAL OPERATORS WITH DOUBLE SYMBOLS 206 4.1.6
BOUNDEDNESS ON L 2 (R N ) 207 4.1.7 CONSEQUENCES OF THE
CALDERON-VAILLANCOURT THEOREM .... 210 4.2 BI-DISCRETIZATION OF
OPERATORS ON L 2 (M. N ) 211 4.2.1 BI-DISCRETIZATION 211 4.2.2
BI-DISCRETIZATION AND FREDHOLMNESS 213 4.2.3 BI-DISCRETIZATION AND LIMIT
OPERATORS 215 4.3 FREDHOLMNESS OF PSEUDODIFFERENTIAL OPERATORS 218 4.3.1
A WIENER ALGEBRA ON L 2 (R N ) 218 4.3.2 FREDHOLMNESS OF OPERATORS IN W
S (L 2 (R N )) 222 4.3.3 FREDHOLM PROPERTIES OF PSEUDODIFFERENTIAL
OPERATORS IN OPS$ 0 224 II CONTENTS 4.4 APPLICATIONS 228 4.4.1 OPERATORS
WITH SLOWLY OSCILLATING SYMBOLS 228 4.4.2 OPERATORS WITH ALMOST PERIODIC
SYMBOLS 230 4.4.3 OPERATORS WITH SEMI-ALMOST PERIODIC SYMBOLS 233 4.4.4
PSEUDODIFFERENTIAL OPERATORS OF NONZERO ORDER 234 4.4.5 DIFFERENTIAL
OPERATORS 236 4.4.6 SCHRODINGER OPERATORS 239 4.4.7 PARTIAL
DIFFERENTIAL-DIFFERENCE OPERATORS 242 4.5 MELLIN PSEUDODIFFERENTIAL
OPERATORS 243 4.5.1 PSEUDODIFFERENTIAL OPERATORS WITH ANALYTIC SYMBOLS
243 4.5.2 MELLIN PSEUDODIFFERENTIAL OPERATORS 247 4.5.3 MELLIN
PSEUDODIFFERENTIAL OPERATORS WITH ANALYTIC SYMBOLS 250 4.5.4 LOCAL
INVERTIBILITY OF MELLIN PSEUDODIFFERENTIAL OPERATORS 251 4.6 SINGULAR
INTEGRALS OVER CARLESON CURVES WITH MUCKENHOUPT WEIGHTS 254 4.6.1
CARLESON CURVES AND MUCKENHOUPT WEIGHTS 254 4.6.2 LOGARITHMIC SPIRALS
AND POWER WEIGHTS 255 4.6.3 CURVES AND WEIGHTS WITH SLOWLY OSCILLATING
DATA 257 4.6.4 LOCAL REPRESENTATIVES AND LOCAL SPECTRA OF SINGULAR
INTEGRAL OPERATORS 258 4.6.5 SINGULAR INTEGRAL OPERATORS ON COMPOSED
CURVES 262 4.7 COMMENTS AND REFERENCES 265 PSEUDODIFFERENCE OPERATORS
5.1 PSEUDODIFFERENCE OPERATORS 267 5.2 FREDHOLMNESS OF PSEUDODIFFERENCE
OPERATORS 273 5.3 FREDHOLM PROPERTIES OF PSEUDODIFFERENCE OPERATORS ON
WEIGHTED SPACES 276 5.3.1 BOUNDEDNESS ON WEIGHTED SPACES 276 5.3.2
FREDHOLMNESS ON WEIGHTED SPACES 278 5.3.3 THE PHRAGMEN-LINDELOF
PRINCIPLE 279 5.4 SLOWLY OSCILLATING PSEUDODIFFERENCE OPERATORS 280
5.4.1 FREDHOLMNESS ON Z P -SPACES 280 5.4.2 FREDHOLMNESS ON WEIGHTED
SPACES, PHRAGMEN-LINDELOF PRINCIPLE 284 5.4.3 FREDHOLM INDEX FOR
OPERATORS IN OPSO 287 5.5 ALMOST PERIODIC PSEUDODIFFERENCE OPERATORS 288
5.6 PERIODIC PSEUDODIFFERENCE OPERATORS 289 5.6.1 THE ONE-DIMENSIONAL
CASE 290 5.6.2 THE MULTI-DIMENSIONAL CASE 292 CONTENTS 5.7 SEMI-PERIODIC
PSEUDODIFFERENCE OPERATORS 293 5.7.1 FREDHOLMNESS ON UNWEIGHTED SPACES
293 5.7.2 FREDHOLMNESS ON WEIGHTED SPACES 296 5.7.3 FREDHOLM INDEX 297
5.8 DISCRETE SCHRODINGER OPERATORS 297 5.8.1 SLOWLY OSCILLATING
POTENTIALS 298 5.8.2 EXPONENTIAL DECAY OF EIGENFUNCTIONS 299 5.8.3
SEMI-PERIODIC SCHRODINGER OPERATORS 301 5.9 COMMENTS AND REFERENCES 302
FINITE SECTIONS OF BAND-DOMINATED OPERATORS 6.1 STABILITY OF THE FINITE
SECTION METHOD 304 6.1.1 APPROXIMATION SEQUENCES 304 6.1.2 STABILITY VS.
INVERTIBILITY 306 6.1.3 STABILITY VS. FREDHOLMNESS 307 6.2 FINITE
SECTIONS OF BAND-DOMINATED OPERATORS ON Z 1 AND Z 2 312 6.2.1
BAND-DOMINATED OPERATORS ON Z 1 : THE GENERAL CASE 313 6.2.2
BAND-DOMINATED OPERATORS ON Z 1 : SLOWLY OSCILLATING COEFFICIENTS 315
6.2.3 BAND-DOMINATED OPERATORS ON Z 2 318 6.2.4 FINITE SECTIONS OF
CONVOLUTION TYPE OPERATORS 320 6.3 SPECTRAL APPROXIMATION 321 6.3.1
WEAKLY SUFFICIENT FAMILIES AND SPECTRA 322 6.3.2 INTERLUDE: SPECTRA OF
BAND-DOMINATED OPERATORS ON HILBERT SPACES 326 6.3.3 ASYMPTOTIC BEHAVIOR
OF NORMS 327 6.3.4 ASYMPTOTIC BEHAVIOR OF SPECTRA 328 6.4 FRACTALITY OF
APPROXIMATION METHODS 332 6.4.1 FRACTAL APPROXIMATION SEQUENCES 333
6.4.2 FRACTALITY AND NORMS 335 6.4.3 FRACTALITY AND SPECTRA 336 6.4.4
FRACTALITY OF THE FINITE SECTION METHOD FOR A CLASS OF BAND-DOMINATED
OPERATORS 339 6.5 COMMENTS AND REFERENCES 342 AXIOMATIZATION OF THE
LIMIT OPERATORS APPROACH 7.1 AN AXIOMATIC APPROACH TO THE LIMIT
OPERATORS METHOD 345 7.2 OPERATORS ON HOMOGENEOUS GROUPS 361 7.2.1
HOMOGENEOUS GROUPS 361 7.2.2 MULTIPLICATION OPERATORS 362 7.2.3
PARTITION OF UNITY 363 7.2.4 CONVOLUTION OPERATORS 364 7.2.5 SHIFT
OPERATORS 365 X CONTENTS 7.3 FREDHOLM CRITERIA FOR CONVOLUTION TYPE
OPERATORS WITH SHIFT 368 7.3.1 OPERATORS ON HOMOGENEOUS GROUPS 368 7.3.2
OPERATORS ON DISCRETE SUBGROUPS 372 7.4 COMMENTS AND REFERENCES 373
BIBLIOGRAPHY 375 INDEX 387
|
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| id | DE-604.BV019439442 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:00:11Z |
| institution | BVB |
| isbn | 3764370815 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012892973 |
| oclc_num | 55587569 |
| open_access_boolean | |
| owner | DE-824 DE-91 DE-BY-TUM DE-11 |
| owner_facet | DE-824 DE-91 DE-BY-TUM DE-11 |
| physical | 392 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Rabinovich, Vladimir Verfasser aut Limit operators and their applications in operator theory Vladimir Rabinovich ; Steffen Roch ; Bernd Silbermann Basel Birkhäuser 2004 392 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 150 Differential operators Fredholm operators Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s DE-604 Roch, Steffen 1958- Verfasser (DE-588)112466737 aut Silbermann, Bernd 1941- Verfasser (DE-588)124151035 aut Operator theory 150 (DE-604)BV000000970 150 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892973&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rabinovich, Vladimir Roch, Steffen 1958- Silbermann, Bernd 1941- Limit operators and their applications in operator theory Operator theory Differential operators Fredholm operators Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | Limit operators and their applications in operator theory |
| title_auth | Limit operators and their applications in operator theory |
| title_exact_search | Limit operators and their applications in operator theory |
| title_full | Limit operators and their applications in operator theory Vladimir Rabinovich ; Steffen Roch ; Bernd Silbermann |
| title_fullStr | Limit operators and their applications in operator theory Vladimir Rabinovich ; Steffen Roch ; Bernd Silbermann |
| title_full_unstemmed | Limit operators and their applications in operator theory Vladimir Rabinovich ; Steffen Roch ; Bernd Silbermann |
| title_short | Limit operators and their applications in operator theory |
| title_sort | limit operators and their applications in operator theory |
| topic | Differential operators Fredholm operators Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Differential operators Fredholm operators Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892973&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
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