Substitution dynamical systems - spectral analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Edition: | 2nd. ed. |
| Series: | Lecture notes in mathematics
1294 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 351 S. |
| ISBN: | 9783642112119 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONTENTS 1 THE BANACH ALGEBRA M (T) 1 1 .1 BASIC DEFINITIONS 1 1.2 THE
GELFAND SPECTRUM A OF M(T) 7 1.2.1 GENERALIZED CHARACTERS 7 1.2.2 BASIC
OPERATIONS 8 1.2.3 TOPOLOGIES ON A (X) 8 1.2.4 CONSTANTS IN A (JU) 9
1.3 GENERALIZED RIESZ PRODUCTS 10 1.4 IDEMPOTENTS IN A AND
DECOMPOSITIONS OF M(T) 14 1.5 DIRICHLET MEASURES 17 2 SPECTRAL THEORY OF
UNITARY OPERATORS 21 2.1 REPRESENTATION THEOREM OF UNITARY OPERATORS 21
2.1.1 CONSTRUCTION OF SPECTRAL MEASURES 21 2.1.2 PROPERTIES OF THE
SPECTRAL FAMILY 22 2.1.3 SPECTRAL REPRESENTATION THEOREM 25 2.1.4
INVARIANT SUBSPACES AND SPECTRAL PROJECTORS 26 2.2 OPERATORS WITH SIMPLE
SPECTRUM 29 2.2.1 BASIC EXAMPLES 29 2.2.2 SIMPLE LEBESGUE SPECTRUM 30
2.3 SPECTRAL DECOMPOSITION THEOREM AND MAXIMAL SPECTRAL TYPE 31 2.4
SPECTRAL DECOMPOSITION THEOREM AND SPECTRAL MULTIPLICITY 34 2.4.1
MULTIPLICITY FUNCTION 35 2.4.2 GLOBAL MULTIPLICITY 37 2.5 EIGENVALUES
AND DISCRETE SPECTRUM 40 2.5.1 EIGENVALUES 40 2.5.2 DISCRETE SPECTRAL
MEASURES 41 2.5.3 BASIC EXAMPLES 43 2.6 APPLICATION TO ERGODIC SEQUENCES
44 3 SPECTRAL THEORY OF DYNAMICAL SYSTEMS 4 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/998455709 DIGITALISIERT DURCH XII
CONTENTS 3.2 ERGODIC DYNAMICAL SYSTEMS 51 3.2.1 FIRST EXAMPLES 51 3.2.2
MAIN THEOREMS 53 3.2.3 QUASI-INVARIANT SYSTEMS 56 3.3 MIXING PROPERTIES
59 3.3.1 WEAK AND STRONG MIXING PROPERTIES 59 3.3.2 MILD MIXING PROPERTY
62 3.3.3 MULTIPLE MIXING PROPERTIES 66 3.4 DISCRETE ERGODIC SYSTEMS 69
3.4.1 VON NEUMANN S THEOREM 69 3.4.2 THE KRONECKER FACTOR 71 3.5 PURITY
LAW AND D-ERGODICITY 73 3.5.1 EXTREMAL PROPERTIES OF ERGODIC
PROBABILITIES 74 3.5.2 D-ERGODICITY 75 3.5.3 APPLICATIONS OF PURITY LAWS
77 3.6 GROUP EXTENSIONS 80 3.6.1 TWO-POINTS EXTENSIONS OF AN IRRATIONAL
ROTATION 81 3.6.2 TWO-POINTS EXTENSIONS OF AN ODOMETER 85 4 DYNAMICAL
SYSTEMS ASSOCIATED WITH SEQUENCES 87 4.1 TOPOLOGICAL DYNAMICAL SYSTEMS
.* 87 4.1.1 MINIMALITY AND TOPOLOGICAL TRANSITIVITY 87 4.1.2 INVARIANT
MEASURES AND UNIQUE ERGODICITY 90 4.1.3 EXAMPLES AND APPLICATION TO
ASYMPTOTIC DISTRIBUTION 93 4.2 DYNAMICAL SYSTEMS ASSOCIATED WITH
FINITELY VALUED SEQUENCES.... 97 4.2.1 SUBSHIFTS 97 4.2.2 MINIMALITY AND
UNIQUE ERGODICITY 98 4.2.3 EXAMPLES 101 4.3 SPECTRAL PROPERTIES OF
BOUNDED SEQUENCES 102 4.3.1 CORRELATION MEASURES 103 4.3.2 APPLICATIONS
OF CORRELATION MEASURES 108 4.3.3 EXAMPLES OF CORRELATION MEASURES 120
4.3.4 BACK TO FINITE-VALUED SEQUENCES 1 23 5 DYNAMICAL SYSTEMS ARISING
FROM SUBSTITUTIONS 12 CONTENTS XIII 5.5 COMBINATORIAL ASPECTS 146 5.5.1
COMPLEXITY FUNCTION AND TOPOLOGICAL ENTROPY 146 5.5.2 RECOGNIZABILITY
PROPERTIES 150 5.6 STRUCTURE OF SUBSTITUTION DYNAMICAL SYSTEMS 152 5.6.1
CONSEQUENCES OF THE RECOGNIZABILITY 152 5.6.2 (X)-INDUCED MAP 154 5.6.3
METRIC PROPERTIES 156 5.6.4 BILATERAL SUBSTITUTION SEQUENCES 159 6
EIGENVALUES OF SUBSTITUTION DYNAMICAL SYSTEMS 161 6.1 EIGENVALUES OF A
CONSTANT-LENGTH SUBSTITUTION 161 6.1.1 CONTINUOUS EIGENVALUES 161 6.1.2
L 2 -EIGENVALUES 164 6.2 EIGENVALUES OF A NONCONSTANT-LENGTH
SUBSTITUTION 169 6.2.1 HOST S THEOREM 169 6.2.2 APPLICATION TO MIXING
PROPERTY 174 6.3 PURE POINT SPECTRUM 176 6.3.1 DISCRETE CONSTANT-LENGTH
SUBSTITUTIONS 176 6.3.2 DISCRETE NONCONSTANT-LENGTH SUBSTITUTIONS 180
6.3.3 PISOT SUBSTITUTIONS 1 87 7 MATRICES OF MEASURES 193 7. 1
CORRELATION MATRIX 193 7.1.1 SPECTRAL MULTIPLICITY 193 7.1.2 MAXIMAL
SPECTRAL TYPE 195 7.1.3 THE CORRELATION MATRIX Z 197 7.2 POSITIVE
DEFINITE MATRICES OF MEASURES 199 7.2.1 DEFINITIONS AND PROPERTIES 199
7.2.2 DECOMPOSITIONS OF MATRICES OF MEASURES 202 7.3 CHARACTERS ON A
MATRIX OF MEASURES 204 8 MATRIX RIESZ PRODUCTS 20 XIV CONTENTS 9.2
SPECTRAL STUDY OF BIJECTIVE SUBSTITUTIONS 232 9.2.1 ABELIAN CASE 233
9.2.2 NON-ABELIAN CASE 235 10 MAXIMAL SPECTRAL TYPE OF GENERAL AUTOMATA
243 10.1 THE COINCIDENCE MATRIX C 243 10.1.1 PROPERTIES OF C 244 10.1.2
EXAMPLES 247 10.2 THE PROJECTION OPERATOR P 248 10.2.1 A PROPERTY OF P
250 10.2.2 EXAMPLES 252 10.3 THE BI-CORRELATION MATRIX Z 254 10.4 MAIN
THEOREM ON MAXIMAL SPECTRAL TYPE 259 11 SPECTRAL MULTIPLICITY OF GENERAL
AUTOMATA 265 11.1 MORE ABOUT THE SPECTRUM OF CONSTANT-LENGTH
SUBSTITUTIONS 265 11.1.1 THE CONVEX SET JFF 265 11.1.2 EXAMPLES 268 11.2
SPECTRAL MULTIPLICITY OF CONSTANT-LENGTH SUBSTITUTIONS 271 11.2.1 MAIN
THEOREM ON SPECTRAL MULTIPLICITY 272 11.2.2 EXAMPLES 275 11.2.3 MORE
ABOUT LEBESGUE MULTIPLICITY 279 12 COMPACT AUTOMATA 281 12.1 STRICTLY
ERGODIC AUTOMATIC FLOWS 281 12.2 APPLICATION TO BOUNDED REMAINDER SETS
286 A SCHROEDINGER OPERATORS WITH SUBSTITUTIVE POTENTIAL 293 A.I
CLASSICAL FACTS ON ID DISCRETE SCHROEDINGER OPERATORS 293 A. 1.1
PRELIMINARIES 293 A. 1.2 SCHROEDINGER EQUATION 295 A. 1.3 PERIODIC
POTENTIAL 299 A.2 ERGODIC FAMILY OF SCHROEDINGER OPERATORS 302 A.2.
CONTENTS XV B.2 MORPHIC NUMBERS 324 B.2.1 SCHMIDT S THEOREM ON
NON-QUADRATIC NUMBERS 324 B.2.2 THE THUE-MORSE CONTINUED FRACTION 328
B.3 SCHMIDT SUBSPACE THEOREM 331 B.3.1 TRANSCENDENCE AND REPETITIONS 332
B.3.2 TRANSCENDENCE AND PALINDROMES 333 REFERENCES 335 GLOSSARY 345
INDEX 347
|
| any_adam_object | 1 |
| author | Queffélec, Martine |
| author_GND | (DE-588)111580048 |
| author_facet | Queffélec, Martine |
| author_role | aut |
| author_sort | Queffélec, Martine |
| author_variant | m q mq |
| building | Verbundindex |
| bvnumber | BV025599736 |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)575066486 (DE-599)BVBBV025599736 |
| dewey-full | 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.39 |
| dewey-search | 515.39 |
| dewey-sort | 3515.39 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd. ed. |
| format | Book |
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| indexdate | 2024-07-09T22:37:15Z |
| institution | BVB |
| isbn | 9783642112119 |
| language | English |
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| oclc_num | 575066486 |
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| owner | DE-11 |
| owner_facet | DE-11 |
| physical | XV, 351 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Queffélec, Martine Verfasser (DE-588)111580048 aut Substitution dynamical systems - spectral analysis Martine Queffélec 2nd. ed. Berlin [u.a.] Springer 2010 XV, 351 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1294 Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Substitution (DE-588)4183925-0 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Spektraltheorie (DE-588)4116561-5 s DE-604 Substitution (DE-588)4183925-0 s Lecture notes in mathematics 1294 (DE-604)BV000676446 1294 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195300&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Queffélec, Martine Substitution dynamical systems - spectral analysis Lecture notes in mathematics Spektraltheorie (DE-588)4116561-5 gnd Dynamisches System (DE-588)4013396-5 gnd Substitution (DE-588)4183925-0 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4013396-5 (DE-588)4183925-0 |
| title | Substitution dynamical systems - spectral analysis |
| title_auth | Substitution dynamical systems - spectral analysis |
| title_exact_search | Substitution dynamical systems - spectral analysis |
| title_full | Substitution dynamical systems - spectral analysis Martine Queffélec |
| title_fullStr | Substitution dynamical systems - spectral analysis Martine Queffélec |
| title_full_unstemmed | Substitution dynamical systems - spectral analysis Martine Queffélec |
| title_short | Substitution dynamical systems - spectral analysis |
| title_sort | substitution dynamical systems spectral analysis |
| topic | Spektraltheorie (DE-588)4116561-5 gnd Dynamisches System (DE-588)4013396-5 gnd Substitution (DE-588)4183925-0 gnd |
| topic_facet | Spektraltheorie Dynamisches System Substitution |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195300&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT queffelecmartine substitutiondynamicalsystemsspectralanalysis |