Difference equations in normed spaces: stability and oscillations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2007
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | North-Holland mathematics studies
206 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 362 S. |
| ISBN: | 0444527133 |
Internformat
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Datensatz im Suchindex
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| adam_text | DIFFERENCE EQUATIONS IN NORMED SPACES STABILITY AND OSCILLATIONS
M.I.GIL BEN GURION UNIVERSITY BEER SHEVA, ISRAEL ELSEVIER AMSTERDAM -
BOSTON - HEIDELBERG - LONDON - NEW YORK - OXFORD PARIS - SAN DIEGO - SAN
FRANCISCO - SINGAPORE - SYDNEY - TOKYO CONTENTS 1. DEFINITIONS AND
PRELIMINARIES 1 1.1. BANACH AND HILBERT SPACES 1 1.2. EXAMPLES OF NORMED
SPACES 3 1.3. LINEAR OPERATORS 4 1.4. EXAMPLES OF DIFFERENCE EQUATIONS 6
1.5. STABILITY NOTIONS 8 1.6. THE COMPARISON PRINCIPLE 9 1.7. LIAPUNOV
FUNCTIONS 12 1.8. ORDERED SPACES AND BANACH LATTICES 15 1.9. THE
ABSTRACT GRONWALL LEMMA 16 1.10. DISCRETE INEQUALITIES IN A BANACH
LATTICE 17 2. CLASSES OF OPERATORS 21 2.1. CLASSIFICATION OF SPECTRA 21
2.2. COMPACT OPERATORS IN A HILBERT SPACE 23 2.3. COMPACT MATRICES 25
2.4. INTEGRAL OPERATORS 28 3. FUNCTIONS OF FINITE MATRICES 33 3.1.
MATRIX-VALUED FUNCTIONS 33 3.2. ESTIMATES FOR THE RESOLVENT 34 3.3.
EXAMPLES 36 3.4. ESTIMATES FOR REGULAR MATRIX FUNCTIONS 37 3.5. PROOF OF
THEOREM 3.2.4 38 3.6. PROOFS OF THEOREMS 3.2.1 AND 3.2.3 40 3.7. PROOF
OF THEOREM 3.4.1 47 3.8. NON-EUCLIDEAN NORMS OF POWERS OF MATRICES 51
3.9. ABSOLUTE VALUES OF MATRIX FUNCTIONS 53 3.10. PROOF OF THEOREM 3.9.1
54 XI XII CONTENTS 4. NORM ESTIMATES FOR OPERATOR FUNCTIONS 57 4.1.
REGULAR OPERATOR FUNCTIONS 57 4.2. FUNCTIONS OF HILBERT-SCHMIDT
OPERATORS 58 4.3. OPERATORS WITH HILBERT-SCHMIDT POWERS 59 4.4.
RESOLVENTS OF NEUMANN-SCHATTEN OPERATORS 61 4.5. FUNCTIONS OF
QUASI-HERMITIAN OPERATORS 62 4.6. FUNCTIONS OF QUASIUNITARY OPERATORS 64
4.7. AUXILIARY RESULTS 66 4.8. EQUALITIES FOR EIGENVALUES 70 4.9. PROOFS
OF THEOREMS 4.2.1, 4.2.2 AND 4.4.1 71 5. SPECTRUM PERTURBATIONS 75 5.1.
ROOTS OF ALGEBRAIC EQUATIONS 75 5.2. ROOTS OF FUNCTIONAL EQUATIONS 76
5.3. SPECTRAL VARIATIONS 78 5.4. PERTURBATIONS OF HILBERT-SCHMIDT
OPERATORS 80 5.5. PERTURBATIONS OF NEUMANN - SCHATTEN OPERATORS 80 5.6.
PERTURBATIONS OF QUASI-HERMITIAN OPERATORS 81 5.7. PERTURBATIONS OF
FINITE MATRICES 83 6. LINEAR EQUATIONS WITH CONSTANT OPERATORS 85 6.1.
HOMOGENEOUS EQUATIONS IN A BANACH SPACE 85 6.2. NONHOMOGENEOUS EQUATIONS
WITH CONSTANT OPERATORS 86 6.3. PERTURBATIONS OF AUTONOMOUS EQUATIONS 87
6.4. EQUATIONS WITH HILBERT-SCHMIDT OPERATORS 89 6.5. EQUATIONS WITH
NEUMANN-SCHATTEN OPERATORS 91 6.6. EQUATIONS WITH NON-COMPACT OPERATORS
93 6.7. EQUATIONS IN FINITE DIMENSIONAL SPACES 94 6.8. Z-TRANSFORM 96
6.9. EXPONENTIAL DICHOTOMY 99 6.10. EQUIVALENT NORMS IN A BANACH SPACE
101 7. LIAPUNOV S TYPE EQUATIONS 105 7.1. SOLUTIONS OF LIAPUNOV S TYPE
EQUATIONS 105 7.2. BOUNDS FOR SOLUTIONS OF LIAPUNOV S TYPE EQUATIONS 107
7.3. EQUIVALENT NORMS IN A HILBERT SPACE 108 7.4. PARTICULAR CASES 110
8. BOUNDS FOR SPECTRAL RADIUSES 113 8.1. PRELIMINARY RESULTS 113 8.2.
HILLE - TAMARKIN MATRICES 114 CONTENTS XIII 8.3. PROOF OF THEOREM 8.2.1
117 8.4. LOWER BOUNDS FOR SPECTRAL RADIUSES 118 8.5. FINITE MATRICES 120
8.6. GENERAL OPERATOR AND BLOCK MATRICES 123 8.7. OPERATOR MATRICES
CLOSE TO TRIANGULAR ONES 124 8.8. PROOF OF THEOREM 8.7.1 126 8.9.
OPERATOR MATRICES WITH NORMAL ENTRIES 128 8.10. SCALAR INTEGRAL
OPERATORS 129 8.11. MATRIX INTEGRAL OPERATORS 137 9. LINEAR EQUATIONS
WITH VARIABLE OPERATORS 143 9.1. EVOLUTION OPERATORS 143 9.2. STABILITY
CONDITIONS 144 9.3. PERTURBATIONS OF EVOLUTION OPERATORS 145 9.4.
EQUATIONS CLOSE TO AUTONOMOUS 149 9.5. LINEAR EQUATIONS WITH MAJORANTS
151 10. LINEAR EQUATIONS WITH SLOWLY VARYING COEFFICIENTS 153 10.1. THE
FREEZING METHOD 153 10.2. PROOF OF THEOREM 10.1.1 155 10.3. EQUATIONS IN
HILBERT SPACES 156 10.4. EQUATIONS IN EUCLIDEAN SPACES 158 10.5.
APPLICATIONS OF THE LIAPUNOV TYPE EQUATION 159 10.6. PROOFS OF LEMMA
10.5.1 AND THEOREM 10.5.2 160 11. NONLINEAR EQUATIONS WITH AUTONOMOUS
LINEAR PARTS 163 11.1. SOLUTION ESTIMATES 163 11.2. PROOF OF THEOREM
11.1.1 164 11.3. STABILITY AND BOUNDEDNESS 166 11.4. STABILITY AND
INSTABILITY BY LINEAR APPROXIMATION 167 11.5. EQUATIONS WITH
HILBERT-SCHMIDT OPERATORS 170 11.6. 2 -NORMS OF SOLUTIONS 170 12.
NONLINEAR EQUATIONS WITH TIME-VARIANT LINEAR PARTS 173 12.1. EQUATIONS
WITH GENERAL LINEAR PARTS 173 12.2. PROOF OF THEOREM 12.1.1 176 12.3.
SLOWLY VARYING EQUATIONS IN A BANACH SPACE 177 12.4. PROOF OF THEOREM
12.3.1 178 12.5. SLOWLY VARYING EQUATIONS IN A HILBERT SPACE 180 12.6.
THE FINITE DIMENSIONAL CASE 182 XIV CONTENTS 12.7. EQUATIONS IN ORDERED
SPACES 12.8. PERTURBATIONS OF NONLINEAR EQUATIONS 13. HIGHER ORDER
LINEAR DIFFERENCE EQUATIONS 13.1. HOMOGENEOUS TIME-INVARIANT EQUATIONS
13.2. NONHOMOGENEOUS TIME-INVARIANT EQUATIONS 13.3. NONAUTONOMOUS
EQUATIONS 13.4. Z 2 -NORMS OF SOLUTIONS 13.5. POSITIVE SOLUTIONS OF
LINEAR EQUATIONS 13.6. PROOF OF THEOREM 13.5.1 14. NONLINEAR HIGHER
ORDER DIFFERENCE EQUATIONS 14.1. GENERAL HIGHER ORDER EQUATIONS 14.2.
THE LUR E TYPE EQUATIONS 14.3. PROOF OF THEOREM 14.2.1 14.4. EQUATIONS
IN EUCLIDEAN SPACES 14.5. THE AIZERMAN TYPE PROBLEM 14.6. PROOFS OF
THEOREM 14.5.2 AND LEMMA 14.5.3 14.7. POSITIVE SOLUTIONS OF NONLINEAR
EQUATIONS 14.8. PROOF OF THEOREM 14.7.1 15. INPUT-TO-STATE STABILITY
15.1. GENERAL EQUATIONS 15.2. EQUATIONS WITH TIME-VARIANT LINEAR PARTS
15.3. EQUATIONS WITH BOUNDED NONLINEARITIES 15.4. INPUT VERSION OF THE
AIZERMAN TYPE PROBLEM 15.5. PROOF OF THEOREM 15.4.1 16. PERIODIC
SOLUTIONS OF DIFFERENCE EQUATIONS AND ORBITAL STABILITY 16.1. LINEAR
AUTONOMOUS EQUATIONS 16.2. LINEAR NONAUTONOMOUS EQUATIONS 16.3.
SEMILINEAR AUTONOMOUS EQUATIONS 16.4. SEMILINEAR NONAUTONOMOUS EQUATIONS
16.5. ESSENTIALLY NONLINEAR EQUATIONS 16.6. EQUATIONS WITH LINEAR
MAJORANTS 16.7. EQUATIONS IN A EUCLIDEAN SPACE 16.8. POSITIVE PERIODIC
SOLUTIONS 16.9. ORBITAL STABILITY CONTENTS 17. DISCRETE VOLTERRA
EQUATIONS IN BANACH SPACES 239 17.1. LINEAR VOLTERRA EQUATIONS 239 17.2.
NONLINEAR RECURRENCE EQUATIONS 241 17.3. PROOF OF THEOREM 17.2.1 242
17.4. CONVOLUTION TYPE VOLTERRA EQUATIONS 244 17.5. LINEAR PERTURBATIONS
OF CONVOLUTION EQUATIONS 246 17.6. NONLINEAR CONVOLUTION TYPE EQUATIONS
247 17.7. OPERATOR PENCILS IN A HILBERT SPACE 248 17.8. PENCILS WITH
HILBERT-SCHMIDT OFF-DIAGONALS 251 17.9. NEUMANN-SCHATTEN PENCILS 252
17.10. STABILITY CONDITIONS 253 17.11. VOLTERRA EQUATIONS IN/ 2 (C) 255
17.12. MULTIPLICATIVE REPRESENTATIONS OF SOLUTIONS 257 17.13. PROOF OF
THEOREM 17.12.1 258 18. CONVOLUTION TYPE VOLTERRA DIFFERENCE EQUATIONS
IN EUCLIDEAN SPACES AND THEIR PERTURBATIONS 261 18.1. CONDITIONS IN
TERMS OF DETERMINANTS 261 18.2. FINITE ORDER ENTIRE MATRIX PENCILS 263
18.3. VARIATIONS OF CHARACTERISTIC VALUES 265 18.4. PROOF OF THEOREM
18.3.1 268 18.5. POLYNOMIAL MATRIX PENCILS 271 18.6. CONDITIONS IN TERMS
OF CHARACTERISTIC VALUES 272 19. STIELTJES DIFFERENTIAL EQUATIONS 275
19.1. PRELIMINARIES 275 19.2. SCALAR LINEAR STIELTJES EQUATIONS 276
19.3. A GRONWALL-LIKE INEQUALITY 279 19.4. THE (I -EXPONENTIAL MATRIX
280 19.5. ESTIMATES FOR THE /I -EXPONENTIAL MATRIX 282 19.6. STABILITY
AND BOUNDEDNESS 283 19.7. EXISTENCE AND UNIQUENESS OF SOLUTIONS 286
19.8. DEPENDENCE ON TIME INTEGRATORS 287 20. VOLTERRA - STIELTJES
EQUATIONS 291 20.1. PRELIMINARIES 291 20.2. SOLUTION ESTIMATES 293 20.3.
PROOF OF THEOREM 20.2.1 294 20.4. THE CONTINUOUS CASE 296 XVI CONTENTS
21. DIFFERENCE EQUATIONS WITH CONTINUOUS TIME 299 21.1. PRELIMINARIES
299 21.2. LINEAR EQUATIONS 300 21.3. NONLINEAR EQUATIONS 301 21.4. PROOF
OF THEOREM 21.3.1 302 21.5. STABILITY AND BOUNDEDNESS 303 21.6.
EQUATIONS IN FINITE DIMENSIONAL SPACES 305 22. STEADY STATES OF
DIFFERENCE EQUATIONS 307 22.1. SPACES WITH GENERALIZED NORMS 307 22.2.
POSITIVE STEADY STATES 310 22.3. PROOF OF THEOREM 22.2.1 311 22.4.
EQUATIONS IN I 2 314 22.5. EQUATIONS IN SPACE C[0,1] 316 22.6. FINITE
SYSTEMS OF SCALAR EQUATIONS 319 APPENDIX A. FUNCTIONS OF NON-COMPACT
OPERATORS 325 23.1. TERMINOLOGY 325 23.2. PROPERTIES OF VOLTERRA
OPERATORS 326 23.3. RESOLVENTS OF P-TRIANGULAR OPERATORS 328 23.4.
REPRESENTATIONS OF NONCOMPACT OPERATORS 331 23.5. PROOF OF THEOREM 4.5.1
332 23.6. PROOF OF THEOREM 4.5.5 333 23.7. PROOF OF THEOREM 4.5.3 334
23.8. REPRESENTATIONS OF REGULAR FUNCTIONS 336 23.9. PROOFS OF THEOREMS
4.6.1 AND 4.6.3 339 NOTES 341 REFERENCES 347 LIST OF MAIN SYMBOLS 359
INDEX 361
|
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| dewey-full | 515.625 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.625 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
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| id | DE-604.BV023824433 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:37:29Z |
| institution | BVB |
| isbn | 0444527133 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017466638 |
| oclc_num | 255638279 |
| open_access_boolean | |
| owner | DE-634 DE-11 DE-20 |
| owner_facet | DE-634 DE-11 DE-20 |
| physical | XVI, 362 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Elsevier |
| record_format | marc |
| series | North-Holland mathematics studies |
| series2 | North-Holland mathematics studies |
| spelling | Gil', Michail I. 1941- Verfasser (DE-588)128577916 aut Difference equations in normed spaces stability and oscillations M. I. Gil' 1. ed. Amsterdam [u.a.] Elsevier 2007 XVI, 362 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematics studies 206 Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Operatorwertige Funktion (DE-588)4352034-0 gnd rswk-swf Normierter Raum (DE-588)4127735-1 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 s Normierter Raum (DE-588)4127735-1 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s Operatorwertige Funktion (DE-588)4352034-0 s DE-604 North-Holland mathematics studies 206 (DE-604)BV000003247 206 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017466638&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gil', Michail I. 1941- Difference equations in normed spaces stability and oscillations North-Holland mathematics studies Differenzengleichung (DE-588)4012264-5 gnd Operatorwertige Funktion (DE-588)4352034-0 gnd Normierter Raum (DE-588)4127735-1 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4012264-5 (DE-588)4352034-0 (DE-588)4127735-1 (DE-588)4167992-1 |
| title | Difference equations in normed spaces stability and oscillations |
| title_auth | Difference equations in normed spaces stability and oscillations |
| title_exact_search | Difference equations in normed spaces stability and oscillations |
| title_full | Difference equations in normed spaces stability and oscillations M. I. Gil' |
| title_fullStr | Difference equations in normed spaces stability and oscillations M. I. Gil' |
| title_full_unstemmed | Difference equations in normed spaces stability and oscillations M. I. Gil' |
| title_short | Difference equations in normed spaces |
| title_sort | difference equations in normed spaces stability and oscillations |
| title_sub | stability and oscillations |
| topic | Differenzengleichung (DE-588)4012264-5 gnd Operatorwertige Funktion (DE-588)4352034-0 gnd Normierter Raum (DE-588)4127735-1 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Differenzengleichung Operatorwertige Funktion Normierter Raum Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017466638&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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