A theory of fractional powers of operators:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2001
|
| Edition: | 1. ed. |
| Series: | North-Holland mathematics studies
187 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 365 S. graph. Darst. |
| ISBN: | 0444887970 |
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MARC
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| 245 | 1 | 0 | |a A theory of fractional powers of operators |c Celso Martínez Carracedo and Miguel Sanz Alix |
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Record in the Search Index
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| adam_text | THE THEORY OF FRACTIONAL POWERS OF OPERATORS CELSO MARTINEZ CARRACEDO
AND MIGUEL SANZ ALIX DEPARTAMENT DE MATEMATICA APLICADA UNIVERSITAT DE
VALENCIA C/DR. MOLINER 50 46100 BURJASSOT VALENCIA SPAIN 2001 ELSEVIER
AMSTERDAM - LONDON - NEW YORK - OXFORD - PARIS - SHANNON - TOKYO
CONTENTS INTRODUCTION IX 1 NON-NEGATIVE OPERATORS 1 1.1 DEFINITION AND
BASIC PROPERTIES 1 1.2 SECTORIAL OPERATORS 6 1.3 EXAMPLES OF
NON-NEGATIVE OPERATORS 8 1.3.1 M-ACCRETIVE OPERATORS 9 1.3.2 NEGATIVE OF
GENERATORS OF SEMIGROUPS 11 1.3.3 PRODUCT OF OPERATORS 12 1.3.4
MULTIPLICATION OPERATORS 12 1.3.5 GENERATION OF SECTORIAL OPERATORS 14
1.3.6 KOMATSU S COUNTEREXAMPLE 16 1.3.7 NORMAL OR SELF-ADJOINT SECTORIAL
OPERATORS 20 1.4 NON-NEGATIVE OPERATORS IN LOCALLY CONVEX SPACES 23
1.4.1 NON-NEGATIVE OPERATORS WHICH ARE NOT SECTORIAL 27 1.5 NOTES ON
CHAPTER 1 29 2 DIFFERENTIAL OPERATORS 31 2.1 OPERATORS OF
RIEMANN-LIOUVILLE AND WEYL 31 2.2 THE DERIVATIVE OPERATOR IN R 35 2.3
THE LAPLACIAN OPERATOR 36 2.4 SECOND-ORDER ELLIPTIC DIFFERENTIAL
OPERATORS 42 2.4.1 CASE 1: P = 2 42 2.4.2 CASE 2: 1 P OO 45 2.4.3
CASE 3: THE OPERATOR A C 48 2.4.4 CASE 4: P = 1 49 2.5 THE LAPLACIAN IN
A LOCALLY CONVEX SPACE OF DISTRIBUTIONS .... 53 2.6 NOTES ON CHAPTER 2
55 3 THE BALAKRISHNAN OPERATOR 57 3.1 DEFINITION OF BALAKRISHNAN AND
BASIC PROPERTIES 57 3.2 EXPRESSIONS OF THE BALAKRISHNAN OPERATOR WHEN *A
IS THE INFIN- ITESIMAL GENERATOR OF AN EQUIBOUNDED CO-SERNIGROUP 66 3.3
EXAMPLES 69 VI CONTENTS 3.4 NOTES ON CHAPTER 3 71 4 AN EXTENSION OF THE
HIRSCH FUNCTIONAL CALCULUS 73 4.1 CLASSES OF FUNCTIONS ASSOCIATED TO
RADON MEASURES 73 4.1.1 DESCRIPTION OF DIFFERENT CLASSES OF FUNCTIONS 73
4.1.2 EXAMPLES 75 4.1.3 UNIQUENESS AND POINTWISE CONVERGENCE 77 4.1.4 A
CHARACTERIZATION OF THE CLASS T+ 80 4.2 FUNCTIONAL CALCULUS 84 4.2.1
DEFINITION AND BASIC PROPERTIES 85 4.2.2 PRODUCT FORMULA 87 4.2.3
STABILITY UNDER COMPOSITION 93 4.3 SPECTRAL MAPPING THEOREM 97 4.4
HIRSCH FUNCTIONAL CALCULUS IN LOCALLY CONVEX SPACES 99 4.4.1 INTEGRATION
IN LOCALLY CONVEX SPACES 99 4.4.2 REMARKS ON THE HIRSCH FUNCTIONAL
CALCULUS IN LOCALLY CONVEX SPACES 102 4.5 NOTES ON CHAPTER 4 10 3 5
FRACTIONAL POWERS OF OPERATORS 105 5.1 DEFINITION OF FRACTIONAL POWER.
ADDITIVITY 105 5.2 REPRESENTATIONS OF THE FRACTIONAL POWERS 114 5.3
SPECTRAL MAPPING THEOREM 116 5.4 SECTORIALITY OF THE FRACTIONAL POWERS.
MULTIPLICATIVITY 123 5.5 SEMIGROUPS GENERATED BY FRACTIONAL POWERS 129
5.6 FRACTIONAL POWERS OF OPERATORS IN LOCALLY CONVEX SPACES . . . . 134
5.7 NOTES ON CHAPTER 5 138 6 DOMAINS, UNIQUENESS AND THE CAUCHY PROBLEM
141 6.1 DOMAINS OF FRACTIONAL POWERS 141 6.1.1 DOMAINS OF THE FRACTIONAL
POWERS WHEN * A GENERATES AN EQUIBOUNDED CO-SEMIGROUP 148 6.2 CONDITIONS
FOR UNIQUENESS 151 6.2.1 SUFFICIENT CONDITIONS FOR UNIQUENESS 152 6.2.2
SPECTRAL AND ANALYTICITY CONDITIONS : 154 6.2.3 N-TH ROOTS OF A
NON-NEGATIVE OPERATOR 157 6.3 THE SECOND - ORDER ABSTRACT INCOMPLETE
CAUCHY PROBLEM . . . . 164 6.4 RESULTS IN LOCALLY CONVEX SPACES 169 6.5
NOTES ON CHAPTER 6 170 7 NEGATIVE AND IMAGINARY POWERS 171 7.1
DEFINITIONS AND BASIC PROPERTIES 171 7.2 THE BALAKRISHNAN AND KOMATSU
OPERATORS 175 7.3 EXAMPLES 178 7.4 LIMIT OPERATORS RELATED TO THE
IMAGINARY POWER 182 7.5 NEGATIVE AND IMAGINARY POWERS ON LOCALLY CONVEX
SPACES . . . . 188 VLL 7.6 NOTES ON CHAPTER 7 189 8 THE DORE-VENNI
THEOREM 191 8.1 DEFINITIONS AND NOTATIONS 191 8.2 SECTORIALITY AND
BOUNDEDNESS OF EXPONENTIAL TYPE 192 8.3 THE DORE VENNI THEOREM R. 200
8.4 SUM OF CLOSED OPERATORS IN UMD SPACES 208 8.5 I? MAXIMAL REGULARITY
214 8.6 NOTES ON CHAPTER 8 216 9 FUNCTIONAL CALCULUS FOR CO-GROUPS 219
9.1 THE MELLIN TRANSFORM 219 9.2 FUNCTIONAL CALCULUS FOR CO-GROUPS 221
9.3 ANALYTIC GENERATORS. IMAGINARY POWERS OF THE PRODUCT 228 9.4
IMAGINARY POWERS OF THE SUM OF OPERATORS 233 9.5 NOTES ON CHAPTER 9 242
10 IMAGINARY POWERS ON HILBERT SPACES 245 10.1 LOGARITHMS 245 10.1.1
RELATIONSHIP BETWEEN POWER ANGLE AND SPECTRAL ANGLE . . 249 10.2 BOUNDED
FUNCTIONAL CALCULUS 251 10.3 NOTES ON CHAPTER 10 255 11 FRACTIONAL
POWERS AND INTERPOLATION SPACES 257 11.1 INTRODUCTION 257 11.2
INTERPOLATION SPACES. THE REAL METHOD 261 11.3 KOMATSU S SPACES 263 11.4
KOMATSU S SPACES AND REAL INTERPOLATION SPACES 268 11.5 DOMAINS OF
FRACTIONAL POWERS AND THE KOMATSU SPACES 270 11.6 INTERPOLATION SPACES.
THE COMPLEX METHOD 273 11.7 NOTES ON CHAPTER 11 277 12 FRACTIONAL POWERS
OF SOME DIFFERENTIAL OPERATORS 279 12.1 IMAGINARY POWERS OF DIFFERENTIAL
POLYNOMIALS IN W (E N ) 279 12.1.1 IMAGINARY POWERS OF DERIVATIVE
OPERATORS 283 12.1.2 IMAGINARY POWERS OF THE NEGATIVE OF THE LAPLACIAN
.... 288 12.2 RIESZ AND BESSEL POTENTIALS 292 12.3 FRACTIONAL SOBOLEV
SPACES 297 12.4 NOTES ON CHAPTER 12 303 A APPENDIX 307 A.I NETS 307 A.2
LINEAR OPERATORS 307 A.3 FUNCTIONAL ANALYSIS 310 A.3.1 BANACH SPACES 310
A.3.2 BANACH ALGEBRAS 312 A.3.3 HILBERT SPACES 313 A.4 MEASURE AND
INTEGRATION 315 A.4.1 * LEBESGUE SPACES 315 A.4.2 THE RADON-RIESZ
REPRESENTATION THEOREM 316 A.4.3 CALCULUS FACTS 319 A.5 THE
STONE-WEIERSTRASS THEOREM 320 A.6 VECTOR-VALUED FUNCTIONS 321 A.6.1
ANALYTIC FUNCTIONS 321 A.6.2 INTEGRATION THEORY FOR VECTOR-VALUED
FUNCTIONS 323 A.7 SEMIGROUPS 326 A. 8 CONVOLUTION AND FOURIER TRANSFORMS
330 A.9 HARMONIC ANALYSIS 333 A.9.1 THE MIKHLIN MULTIPLIER THEOREM 333
A.9.2 THE RIESZ-THORIN CONVEXITY THEOREM 334 A. 10 DISTRIBUTIONS 335
A.LL SOBOLEV SPACES 337 NOTATIONS 341 BIBLIOGRAPHY 346 VIA
|
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| edition | 1. ed. |
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| isbn | 0444887970 |
| language | English |
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| physical | XI, 365 S. graph. Darst. |
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| series | North-Holland mathematics studies |
| series2 | North-Holland mathematics studies |
| spelling | Martínez Carracedo, Celso Verfasser aut A theory of fractional powers of operators Celso Martínez Carracedo and Miguel Sanz Alix 1. ed. Amsterdam [u.a.] Elsevier 2001 XI, 365 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematics studies 187 Fractional powers Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s DE-604 Sanz Alix, Miguel Verfasser aut North-Holland mathematics studies 187 (DE-604)BV000003247 187 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009902099&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martínez Carracedo, Celso Sanz Alix, Miguel A theory of fractional powers of operators North-Holland mathematics studies Fractional powers Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | A theory of fractional powers of operators |
| title_auth | A theory of fractional powers of operators |
| title_exact_search | A theory of fractional powers of operators |
| title_full | A theory of fractional powers of operators Celso Martínez Carracedo and Miguel Sanz Alix |
| title_fullStr | A theory of fractional powers of operators Celso Martínez Carracedo and Miguel Sanz Alix |
| title_full_unstemmed | A theory of fractional powers of operators Celso Martínez Carracedo and Miguel Sanz Alix |
| title_short | A theory of fractional powers of operators |
| title_sort | a theory of fractional powers of operators |
| topic | Fractional powers Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Fractional powers Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009902099&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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