One-dimensional functional equations
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2003
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| Schriftenreihe: | Operator theory, advances and applications
144 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a One-dimensional functional equations |c G. Belitskii ; V. Tkachenko |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2003 | |
| 300 | |a XIV, 206 S. | ||
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| 490 | 1 | |a Operator theory, advances and applications |v 144 | |
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Datensatz im Suchindex
| _version_ | 1819789006523596800 |
|---|---|
| adam_text | ONE-DIMENSIONAL FUNCTIONAL EQUATIONS G. BELITSKII V. TKACHENKO
BIRKHAEUSER VERLAG BASEL * BOSTON * BERLIN CONTENTS PREFACE IX 1 IMPLICIT
FUNCTIONS 1 1.1 FORMAL SOLVABILITY 2 1.2 THEOREM ON LOCAL SOLVABILITY 3
1.3 TRANSFORMATIONS OF EQUATIONS 4 1.4 GLOBAL SOLVABILITY 6 1.5 COMMENTS
AND REFERENCES 7 2 CLASSIFICATION OF ONE-DIMENSIONAL MAPPINGS 9 2.1
WANDERING AND NON-WANDERING SUBSETS 12 2.2 MAPPINGS WITH WANDERING
COMPACT SETS 14 2.2.1 STRICTLY MONOTONIC MAPPINGS WITHOUT FIXED POINTS
14 2.2.2 THE ABEL AND COHOMOLOGICAL EQUATIONS 16 2.2.3 SMOOTH AND
ANALYTIC SOLUTIONS OF A COHOMOLOGICAL EQUATION 20 2.3 LOCAL STRUCTURE OF
MAPPINGS AT AN ISOLATED FIXED POINT 22 2.3.1 FORMAL CLASSIFICATION 26
2.3.2 SMOOTH CLASSIFICATION 29 2.3.3 ANALYTIC CLASSIFICATION 39 2.4
DIFFEOMORPHISMS WITH ISOLATED FIXED POINTS 46 2.4.1 TOPOLOGICAL
CLASSIFICATION 46 2.4.2 SMOOTH CLASSIFICATION OF DIFFEOMORPHISMS WITH A
UNIQUE FIXED POINT 47 2.4.3 SMOOTH CLASSIFICATION OF DIFFEOMORPHISMS
WITH SEVERAL HYPERBOLIC FIXED POINTS 51 2.4.4 ANOTHER APPROACH TO SMOOTH
CLASSIFICATION 55 2.5 ONE-DIMENSIONAL FLOWS AND VECTOR FIELDS 58 2.5.1
CLASSIFICATION OF VECTOR FIELDS IN A NEIGHBORHOOD OF A SINGULAR POINT 61
2.5.2 FLOWS ON THE REAL LINE WITH HYPERBOLIC FIXED POINTS 64 VI CONTENTS
2.6 EMBEDDING PROBLEM AND ITERATIVE ROOTS 68 2.6.1 MAPPINGS WITHOUT
NON-WANDERING POINTS 68 2.6.2 C-EMBEDDING 68 2.6.3 DIFFEOMORPHISMS WITH
A UNIQUE FIXED POINT 69 2.6.4 DIFFEOMORPHISMS WITH SEVERAL FIXED POINTS
72 2.7 COMMENTS AND REFERENCES 74 3 GENERALIZED ABEL EQUATION 77 3.1
LOCAL SOLVABILITY 78 3.1.1 LOCAL SOLVABILITY IN A NEIGHBORHOOD OF A
NON-FIXED POINT . . 78 3.1.2 PROOF OF THEOREM 3.1 FOR ANALYTIC FUNCTIONS
81 3.1.3 LOCAL SOLVABILITY AT AN ISOLATED FIXED POINT 90 3.1.4 MORE ON
ANALYTIC SOLUTIONS 106 3.2 GLOBAL SOLUTIONS OF EQUATIONS WITH NOT MORE
THAN ONE FIXED POINT . 110 3.2.1 EQUATIONS WITH FIXED-POINT FREE
MAPPINGS F 110 3.2.2 THE CASE OF A SINGLE FIXED POINT 113 3.3 GLUING
METHOD FOR LINEAR EQUATIONS WITH SEVERAL FIXED POINTS . . . . 120 3.3.1
COHOMOLOGICAL EQUATION 123 3.3.2 EQUATIONS WITH HYPERBOLIC FIXED POINTS
125 3.4 COMMENTS AND REFERENCES 131 4 EQUATIONS WITH SEVERAL
TRANSFORMATIONS OF ARGUMENT 133 4.1 LOCAL SOLVABILITY 133 4.2 EXTENSION
OF SOLUTIONS 136 4.2.1 ABSORBERS 136 4.2.2 EXTENSION OF SOLUTIONS FROM
AN ABSORBER 137 4.2.3 EXTENSION FROM INTERSECTION OF ABSORBERS.
DECOMPOSITION METHOD 139 4.3 EXAMPLES 142 4.4 DIFFERENCE EQUATIONS IN
CARLEMAN CLASSES 147 4.4.1 DECOMPOSITION IN CLASSES C(M N ) 148 4.4.2
EQUATIONS WITH CONSTANT COEFFICIENTS 150 4.4.3 EQUATIONS WITH
NON-CONSTANT COEFFICIENTS 152 4.5 COMMENTS AND REFERENCES 154 5 LINEAR
EQUATIONS 157 5.1 GENERALIZED LINEAR ABEL EQUATION 162 5.1.1 EQUATIONS
ON THE REAL LINE WITH A UNIQUE FIXED POINT .... 164 5.1.2 COHOMOLOGICAL
EQUATION 167 5.1.3 SPECTRUM OF A WEIGHTED SHIFT OPERATOR 169 5.1.4
NORMAL SOLVABILITY OF EQUATIONS WITH HYPERBOLIC FIXED POINTS 172 5.1.5
EQUATIONS WITH PERIODIC POINTS 177 CONTENTS VII 5.2 LOCALIZATION OF
OBSTACLES TO SOLVABILITY 181 5.3 EQUATIONS WITH CONSTANT COEFFICIENTS
185 5.4 EQUATION WITH AFFINE TRANSFORMATIONS OF ARGUMENT 190 5.5
COMMENTS AND REFERENCES 199 BIBLIOGRAPHY 201 INDEX 207
|
| any_adam_object | 1 |
| author | Belickij, Genrich R. 1941- Tkačenko, Vadim P. |
| author_GND | (DE-588)112018017 |
| author_facet | Belickij, Genrich R. 1941- Tkačenko, Vadim P. |
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| building | Verbundindex |
| bvnumber | BV017172991 |
| callnumber-first | Q - Science |
| callnumber-label | QA431 |
| callnumber-raw | QA431 |
| callnumber-search | QA431 |
| callnumber-sort | QA 3431 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 580 SK 600 |
| ctrlnum | (OCoLC)52257728 (DE-599)BVBBV017172991 |
| dewey-full | 515/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7 |
| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017172991 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T16:17:47Z |
| institution | BVB |
| isbn | 3764300841 |
| language | English |
| lccn | 2003052195 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010351949 |
| oclc_num | 52257728 |
| open_access_boolean | |
| owner | DE-703 DE-11 DE-188 |
| owner_facet | DE-703 DE-11 DE-188 |
| physical | XIV, 206 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory, advances and applications |
| series2 | Operator theory, advances and applications |
| spellingShingle | Belickij, Genrich R. 1941- Tkačenko, Vadim P. One-dimensional functional equations Operator theory, advances and applications Functional equations Dimension 1 (DE-588)4323094-5 gnd Funktionalgleichung (DE-588)4018923-5 gnd |
| subject_GND | (DE-588)4323094-5 (DE-588)4018923-5 |
| title | One-dimensional functional equations |
| title_auth | One-dimensional functional equations |
| title_exact_search | One-dimensional functional equations |
| title_full | One-dimensional functional equations G. Belitskii ; V. Tkachenko |
| title_fullStr | One-dimensional functional equations G. Belitskii ; V. Tkachenko |
| title_full_unstemmed | One-dimensional functional equations G. Belitskii ; V. Tkachenko |
| title_short | One-dimensional functional equations |
| title_sort | one dimensional functional equations |
| topic | Functional equations Dimension 1 (DE-588)4323094-5 gnd Funktionalgleichung (DE-588)4018923-5 gnd |
| topic_facet | Functional equations Dimension 1 Funktionalgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010351949&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT belickijgenrichr onedimensionalfunctionalequations AT tkacenkovadimp onedimensionalfunctionalequations |