The role of the spectrum in the cyclic behavior of composition operators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2004
|
| Series: | Memoirs of the American Mathematical Society
791 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 167, number 791 (first of 5 numbers)." Includes bibliographical references |
| Physical Description: | X, 81 S. |
| ISBN: | 0821834320 |
Staff View
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| 245 | 1 | 0 | |a The role of the spectrum in the cyclic behavior of composition operators |c Eva A. Gallardo-Gutiérrez ; Alfonso Montes-Rodríguez |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2004 | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 791 | |
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Record in the Search Index
| _version_ | 1804130315491344384 |
|---|---|
| adam_text | CONTENTS
Preface ;x
Chapter 1. Introduction and Preliminaries 1
Weighted Hardy spaces 1
The Dirichlet space 2
The Hardy space 2
Functional Hilbert spaces 2
Composition operators 3
Weighted Dirichlet spaces 3
Equivalent norms on weighted Dirichlet spaces 3
Linear fractional maps 4
Iterates 5
The Comparison Principle 6
Main results 7
Table I 8
Table II 10
Acknowledgment 12
Chapter 2. Linear Fractional Maps with an Interior Fixed Point 13
Non elliptic linear fractional maps with an exterior fixed point 13
Elliptic automorphism 17
Interior and boundary fixed point 19
Hypercyclicity 23
The hyperbolic automorphism 24
The Hypercyclic Criterion 24
A Beurling type theorem 25
The Inner Product Criterion 25
Invariant subspaces of finite codimension 31
Chapter 3. Non Elliptic Automorphisms 35
Hypercyclicity 34
The parabolic automorphism 36
The hyperbolic automorphism 38
The failure of the spectrum 40
The eigenfunctions of C^ with p a parabolic automorphism 42
Cyclicity 43
The Dirichlet space of the upper half plane 44
The Hardy space of the upper half plane 44
A Paley Wiener Theorem for Vw 44
v
vi CONTENTS
The parabolic automorphism 45
The hyperbolic automorphism 46
Chapter 4. The Parabolic Non Automorphism 48
Cyclicity 48
Zeros of weighted Dirichlet functions 51
Non hypercyclicity 52
An appetizer 52
The spectrum of Cv 53
The eigenfunctions form a spanning set 53
Renorming Sv 54
Isometric functional Hilbert spaces 55
A complete orthogonal system of L2(R+, dt/t) 56
The extension of the isometries 59
The Laguerre polynomials 60
Chapter 5. Supercyclic Linear Fractional Composition Operators 66
The easy part 66
The parabolic non automorphism 68
The Angle Criterion 68
The adjoint of Cv 69
A three term recurrence formula 71
An integration formula 71
Endnotes 77
Bibliography 79
|
| any_adam_object | 1 |
| author | Gallardo-Gutiérrez, Eva A. 1973- |
| author_GND | (DE-588)173672671 (DE-588)17367268X |
| author_facet | Gallardo-Gutiérrez, Eva A. 1973- |
| author_role | aut |
| author_sort | Gallardo-Gutiérrez, Eva A. 1973- |
| author_variant | e a g g eag eagg |
| building | Verbundindex |
| bvnumber | BV017536824 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017536824 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:19:05Z |
| institution | BVB |
| isbn | 0821834320 |
| language | English |
| lccn | 2003061940 |
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| physical | X, 81 S. |
| publishDate | 2004 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Gallardo-Gutiérrez, Eva A. 1973- Verfasser (DE-588)173672671 aut The role of the spectrum in the cyclic behavior of composition operators Eva A. Gallardo-Gutiérrez ; Alfonso Montes-Rodríguez Providence, R.I. American Mathematical Society 2004 X, 81 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 791 "Volume 167, number 791 (first of 5 numbers)." Includes bibliographical references Functieruimten gtt Funções hipergeométricas larpcal Hypergeometrische functies gtt Lineaire operatoren gtt Operadores lineares larpcal Operatortheorie gtt Function spaces Functions of complex variables Hypergeometric functions Linear operators Hypergeometrische Reihe (DE-588)4161061-1 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s Funktionenraum (DE-588)4134834-5 s DE-604 Komplexe Variable (DE-588)4164905-9 s Hypergeometrische Reihe (DE-588)4161061-1 s b DE-604 Montes-Rodríguez, Alfonso 1961- Sonstige (DE-588)17367268X oth Memoirs of the American Mathematical Society 791 (DE-604)BV008000141 791 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010557178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gallardo-Gutiérrez, Eva A. 1973- The role of the spectrum in the cyclic behavior of composition operators Memoirs of the American Mathematical Society Functieruimten gtt Funções hipergeométricas larpcal Hypergeometrische functies gtt Lineaire operatoren gtt Operadores lineares larpcal Operatortheorie gtt Function spaces Functions of complex variables Hypergeometric functions Linear operators Hypergeometrische Reihe (DE-588)4161061-1 gnd Linearer Operator (DE-588)4167721-3 gnd Komplexe Variable (DE-588)4164905-9 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4161061-1 (DE-588)4167721-3 (DE-588)4164905-9 (DE-588)4134834-5 |
| title | The role of the spectrum in the cyclic behavior of composition operators |
| title_auth | The role of the spectrum in the cyclic behavior of composition operators |
| title_exact_search | The role of the spectrum in the cyclic behavior of composition operators |
| title_full | The role of the spectrum in the cyclic behavior of composition operators Eva A. Gallardo-Gutiérrez ; Alfonso Montes-Rodríguez |
| title_fullStr | The role of the spectrum in the cyclic behavior of composition operators Eva A. Gallardo-Gutiérrez ; Alfonso Montes-Rodríguez |
| title_full_unstemmed | The role of the spectrum in the cyclic behavior of composition operators Eva A. Gallardo-Gutiérrez ; Alfonso Montes-Rodríguez |
| title_short | The role of the spectrum in the cyclic behavior of composition operators |
| title_sort | the role of the spectrum in the cyclic behavior of composition operators |
| topic | Functieruimten gtt Funções hipergeométricas larpcal Hypergeometrische functies gtt Lineaire operatoren gtt Operadores lineares larpcal Operatortheorie gtt Function spaces Functions of complex variables Hypergeometric functions Linear operators Hypergeometrische Reihe (DE-588)4161061-1 gnd Linearer Operator (DE-588)4167721-3 gnd Komplexe Variable (DE-588)4164905-9 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Functieruimten Funções hipergeométricas Hypergeometrische functies Lineaire operatoren Operadores lineares Operatortheorie Function spaces Functions of complex variables Hypergeometric functions Linear operators Hypergeometrische Reihe Linearer Operator Komplexe Variable Funktionenraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010557178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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