Complex analysis: the geometric viewpoint
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[Washington, DC]
Math. Assoc. of America
2004
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | The Carus mathematical monographs
23 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 212 S. graph. Darst. |
| ISBN: | 9780883850350 0883850001 |
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Datensatz im Suchindex
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| adam_text |
THE CARUS MATHEMATICAL MONOGRAPHS NUMBER TWENTY-THREE * COMPLEX
ANALYSIS: THE GEOMETRIC VIEWPOINT SECOND EDITION STEVEN G. KRANTZ
WASHINGTON UNIVERSITY IN ST. LOUIS PUBLISHED AND DISTRIBUTED BY THE
MATHEMATICAL ASSOCIATION OF AMERICA CONTENTS ACKNOWLEDGMENTS IX PREFACE
TO THE SECOND EDITION XI PREFACE TO THE FIRST EDITION XIII PRINCIPAL
IDEAS OF CLASSICAL FUNCTION THEORY 1 1. A GLIMPSE OF COMPLEX ANALYSIS 1
2. THE MAXIMUM PRINCIPLE, THE SCHWARZ LEMMA, AND APPLICATIONS 11 3.
NORMAL FAMILIES AND THE RIEMANN MAPPING THEOREM. 16 4. ISOLATED
SINGULARITIES AND THE THEOREMS OF PICARD 22 BASIC NOTIONS OF
DIFFERENTIAL GEOMETRY 29 0. INTRODUCTORY REMARKS 29 1. RIEMANNIAN
METRICS AND THE CONCEPT OF LENGTH 30 2. CALCULUS IN THE COMPLEX DOMAIN
38 3. ISOMETRIES 42 4. THE POINCARE METRIC 45 5. THE SCHWARZ LEMMA 55 6.
A DETOUR INTO NON-EUCLIDEAN GEOMETRY 58 XV XVI CONTENTS 2 CURVATURE AND
APPLICATIONS 67 1. CURVATURE AND THE SCHWARZ LEMMA REVISITED 67 2.
LIOUVILLE'S THEOREM AND OTHER APPLICATIONS 73 3. NORMAL FAMILIES AND THE
SPHERICAL METRIC 79 4. A GENERALIZATION OF MONTEL'S THEOREM AND THE
GREAT PICARD THEOREM 86 3 SOME NEW INVARIANT METRICS 89 0. INTRODUCTORY
REMARKS 89 1. THE CARATHEODORY METRIC 90 2. THE KOBAYASHI METRIC 93 3.
COMPLETENESS OF THE CARATHEODORY AND KOBAYASHI METRICS 103 4. AN
APPLICATION OF COMPLETENESS: AUTOMORPHISMS 121 5. HYPERBOLICITY AND
CURVATURE 133 4 INTRODUCTION TO THE BERGMAN THEORY 137 0. INTRODUCTORY
REMARKS 137 1. BERGMAN BASICS 138 2. INVARIANCE PROPERTIES OF THE
BERGMAN KERNEL 140 3. CALCULATION OF THE BERGMAN KERNEL 143 4. ABOUT THE
BERGMAN METRIC 151 5. MORE ON THE BERGMAN METRIC 155 6. APPLICATION TO
CONFORMAL MAPPING 156 5 A GLIMPSE OF SEVERAL COMPLEX VARIABLES 161 0.
FUNCTIONS OF SEVERAL COMPLEX VARIABLES 161 1. BASIC CONCEPTS 164 2. THE
AUTOMORPHISM GROUPS OF THE BALL AND BIDISC 170 3. INVARIANT METRICS AND
THE INEQUIVALENCE OF THE BALL AND THE BIDISC 180 CONTENTS XVII APPENDIX
191 1. INTRODUCTION 191 2. EXPRESSING CURVATURE INTRINSICALLY 191 3.
CURVATURE CALCULATIONS ON PLANAR DOMAINS 200 SYMBOLS 205 REFERENCES 209
INDEX 213 |
| adam_txt |
THE CARUS MATHEMATICAL MONOGRAPHS NUMBER TWENTY-THREE * COMPLEX
ANALYSIS: THE GEOMETRIC VIEWPOINT SECOND EDITION STEVEN G. KRANTZ
WASHINGTON UNIVERSITY IN ST. LOUIS PUBLISHED AND DISTRIBUTED BY THE
MATHEMATICAL ASSOCIATION OF AMERICA CONTENTS ACKNOWLEDGMENTS IX PREFACE
TO THE SECOND EDITION XI PREFACE TO THE FIRST EDITION XIII PRINCIPAL
IDEAS OF CLASSICAL FUNCTION THEORY 1 1. A GLIMPSE OF COMPLEX ANALYSIS 1
2. THE MAXIMUM PRINCIPLE, THE SCHWARZ LEMMA, AND APPLICATIONS 11 3.
NORMAL FAMILIES AND THE RIEMANN MAPPING THEOREM. 16 4. ISOLATED
SINGULARITIES AND THE THEOREMS OF PICARD 22 BASIC NOTIONS OF
DIFFERENTIAL GEOMETRY 29 0. INTRODUCTORY REMARKS 29 1. RIEMANNIAN
METRICS AND THE CONCEPT OF LENGTH 30 2. CALCULUS IN THE COMPLEX DOMAIN
38 3. ISOMETRIES 42 4. THE POINCARE METRIC 45 5. THE SCHWARZ LEMMA 55 6.
A DETOUR INTO NON-EUCLIDEAN GEOMETRY 58 XV XVI CONTENTS 2 CURVATURE AND
APPLICATIONS 67 1. CURVATURE AND THE SCHWARZ LEMMA REVISITED 67 2.
LIOUVILLE'S THEOREM AND OTHER APPLICATIONS 73 3. NORMAL FAMILIES AND THE
SPHERICAL METRIC 79 4. A GENERALIZATION OF MONTEL'S THEOREM AND THE
GREAT PICARD THEOREM 86 3 SOME NEW INVARIANT METRICS 89 0. INTRODUCTORY
REMARKS 89 1. THE CARATHEODORY METRIC 90 2. THE KOBAYASHI METRIC 93 3.
COMPLETENESS OF THE CARATHEODORY AND KOBAYASHI METRICS 103 4. AN
APPLICATION OF COMPLETENESS: AUTOMORPHISMS 121 5. HYPERBOLICITY AND
CURVATURE 133 4 INTRODUCTION TO THE BERGMAN THEORY 137 0. INTRODUCTORY
REMARKS 137 1. BERGMAN BASICS 138 2. INVARIANCE PROPERTIES OF THE
BERGMAN KERNEL 140 3. CALCULATION OF THE BERGMAN KERNEL 143 4. ABOUT THE
BERGMAN METRIC 151 5. MORE ON THE BERGMAN METRIC 155 6. APPLICATION TO
CONFORMAL MAPPING 156 5 A GLIMPSE OF SEVERAL COMPLEX VARIABLES 161 0.
FUNCTIONS OF SEVERAL COMPLEX VARIABLES 161 1. BASIC CONCEPTS 164 2. THE
AUTOMORPHISM GROUPS OF THE BALL AND BIDISC 170 3. INVARIANT METRICS AND
THE INEQUIVALENCE OF THE BALL AND THE BIDISC 180 CONTENTS XVII APPENDIX
191 1. INTRODUCTION 191 2. EXPRESSING CURVATURE INTRINSICALLY 191 3.
CURVATURE CALCULATIONS ON PLANAR DOMAINS 200 SYMBOLS 205 REFERENCES 209
INDEX 213 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Krantz, Steven G. 1951- |
| author_GND | (DE-588)130535907 |
| author_facet | Krantz, Steven G. 1951- |
| author_role | aut |
| author_sort | Krantz, Steven G. 1951- |
| author_variant | s g k sg sgk |
| building | Verbundindex |
| bvnumber | BV035154090 |
| classification_rvk | SK 750 |
| classification_tum | MAT 303f MAT 530f MAT 320f |
| ctrlnum | (OCoLC)633696323 (DE-599)BVBBV035154090 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| era | Geschichte 1963-1980 gnd Geschichte 1950-1962 gnd Geschichte 1947-1949 gnd |
| era_facet | Geschichte 1963-1980 Geschichte 1950-1962 Geschichte 1947-1949 |
| format | Book |
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| genre | (DE-588)4179998-7 Monografische Reihe gnd-content |
| genre_facet | Monografische Reihe |
| id | DE-604.BV035154090 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:47:56Z |
| indexdate | 2025-01-10T19:02:03Z |
| institution | BVB |
| isbn | 9780883850350 0883850001 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016961298 |
| oclc_num | 633696323 |
| open_access_boolean | |
| owner | DE-20 DE-B768 DE-91G DE-BY-TUM |
| owner_facet | DE-20 DE-B768 DE-91G DE-BY-TUM |
| physical | XV, 212 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Math. Assoc. of America |
| record_format | marc |
| series | The Carus mathematical monographs |
| series2 | The Carus mathematical monographs |
| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut Complex analysis the geometric viewpoint Steven G. Krantz 2. ed. [Washington, DC] Math. Assoc. of America 2004 XV, 212 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Carus mathematical monographs 23 Geschichte 1963-1980 gnd rswk-swf Geschichte 1950-1962 gnd rswk-swf Geschichte 1947-1949 gnd rswk-swf Einfache Gruppe (DE-588)4123107-7 gnd rswk-swf Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Schwarzsche Differentialinvariante (DE-588)4180361-9 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Elektrisches Netzwerk (DE-588)4014214-0 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Kugelpackung (DE-588)4165929-6 gnd rswk-swf (DE-588)4179998-7 Monografische Reihe gnd-content Differentialgeometrie (DE-588)4012248-7 s Funktionentheorie (DE-588)4018935-1 s DE-604 Fehlerkorrekturcode (DE-588)4124917-3 s Geschichte 1947-1949 z Einfache Gruppe (DE-588)4123107-7 s Geschichte (DE-588)4020517-4 s Kugelpackung (DE-588)4165929-6 s Geschichte 1950-1962 z Geschichte 1963-1980 z Ergodentheorie (DE-588)4015246-7 s Zahlentheorie (DE-588)4067277-3 s Elektrisches Netzwerk (DE-588)4014214-0 s Irrfahrtsproblem (DE-588)4162442-7 s Schwarzsche Differentialinvariante (DE-588)4180361-9 s The Carus mathematical monographs 23 (DE-604)BV001887236 23 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016961298&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krantz, Steven G. 1951- Complex analysis the geometric viewpoint The Carus mathematical monographs Einfache Gruppe (DE-588)4123107-7 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd Schwarzsche Differentialinvariante (DE-588)4180361-9 gnd Ergodentheorie (DE-588)4015246-7 gnd Geschichte (DE-588)4020517-4 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd Elektrisches Netzwerk (DE-588)4014214-0 gnd Zahlentheorie (DE-588)4067277-3 gnd Funktionentheorie (DE-588)4018935-1 gnd Kugelpackung (DE-588)4165929-6 gnd |
| subject_GND | (DE-588)4123107-7 (DE-588)4162442-7 (DE-588)4180361-9 (DE-588)4015246-7 (DE-588)4020517-4 (DE-588)4124917-3 (DE-588)4012248-7 (DE-588)4014214-0 (DE-588)4067277-3 (DE-588)4018935-1 (DE-588)4165929-6 (DE-588)4179998-7 |
| title | Complex analysis the geometric viewpoint |
| title_auth | Complex analysis the geometric viewpoint |
| title_exact_search | Complex analysis the geometric viewpoint |
| title_exact_search_txtP | Complex analysis the geometric viewpoint |
| title_full | Complex analysis the geometric viewpoint Steven G. Krantz |
| title_fullStr | Complex analysis the geometric viewpoint Steven G. Krantz |
| title_full_unstemmed | Complex analysis the geometric viewpoint Steven G. Krantz |
| title_short | Complex analysis |
| title_sort | complex analysis the geometric viewpoint |
| title_sub | the geometric viewpoint |
| topic | Einfache Gruppe (DE-588)4123107-7 gnd Irrfahrtsproblem (DE-588)4162442-7 gnd Schwarzsche Differentialinvariante (DE-588)4180361-9 gnd Ergodentheorie (DE-588)4015246-7 gnd Geschichte (DE-588)4020517-4 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd Elektrisches Netzwerk (DE-588)4014214-0 gnd Zahlentheorie (DE-588)4067277-3 gnd Funktionentheorie (DE-588)4018935-1 gnd Kugelpackung (DE-588)4165929-6 gnd |
| topic_facet | Einfache Gruppe Irrfahrtsproblem Schwarzsche Differentialinvariante Ergodentheorie Geschichte Fehlerkorrekturcode Differentialgeometrie Elektrisches Netzwerk Zahlentheorie Funktionentheorie Kugelpackung Monografische Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016961298&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001887236 |
| work_keys_str_mv | AT krantzsteveng complexanalysisthegeometricviewpoint |