Geometric function theory in one and higher dimensions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
2003
|
| Schriftenreihe: | Pure and applied mathematics
255 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 530 S. graph. Darst. |
| ISBN: | 0824709764 |
Internformat
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| 245 | 1 | 0 | |a Geometric function theory in one and higher dimensions |c Ian Graham ; Gabriela Kohr |
| 264 | 1 | |a New York [u.a.] |b Dekker |c 2003 | |
| 300 | |a XV, 530 S. |b graph. Darst. | ||
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| 650 | 4 | |a Fonctions univalentes | |
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| 650 | 4 | |a Functions of several complex variables | |
| 650 | 4 | |a Geometric function theory | |
| 650 | 4 | |a Univalent functions | |
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Datensatz im Suchindex
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| adam_text | GEOMETRIC FUNCTION THEORY IN ONE AND HIGHER DIMENSIONS IAN GRAHAM JWIM^
GABRIELA KOHR UNIY E RSITY-OFTPM$O^I ^XXI » BABES-BOLYAI UNIVERSITY
TORONTO, ONTARIO, !ANADA$L / * CLUJ-NAPOCA, ROMANIA MARCEL DEKKER, INC.
NEW YORK * BASEL CONTENTS PREFACE V INTRODUCTION XIII I UNIVALENT
FUNCTIONS 1 1 ELEMENTARY PROPERTIES OF UNIVALENT FUNCTIONS 3 1.1
UNIVALENCE IN THE COMPLEX PLANE 3 1.1.1 ELEMENTARY RESULTS IN THE THEORY
OF UNIVALENT FUNCTIONS. EXAMPLES OF UNIVALENT FUNCTIONS 3 1.1.2 THE AREA
THEOREM 9 1.1.3 GROWTH, COVERING AND DISTORTION RESULTS IN THE CLASS 5 .
13 1.1.4 THE MAXIMUM MODULUS OF UNIVALENT FUNCTIONS 18 1.1.5 TWO-POINT
DISTORTION RESULTS FOR THE CLASS S 21 2 SUBCLASSES OF UNIVALENT
FUNCTIONS IN THE UNIT DISC 27 2.1 FUNCTIONS WITH POSITIVE REAL PART.
SUBORDINATION AND THE HER- GLOTZ FORMULA 27 2.1.1 THE CARATHEODORY
CLASS. SUBORDINATION 27 2.1.2 APPLICATIONS OF THE SUBORDINATION
PRINCIPLE 32 2.2 STARLIKE AND CONVEX FUNCTIONS 36 2.3 STARLIKENESS AND
CONVEXITY OF ORDER A. ALPHA CONVEXITY 54 2.3.1 STARLIKENESS AND
CONVEXITY OF ORDER A 54 2.3.2 ALPHA CONVEXITY 58 VII VIII CONTENTS 2.4
CLOSE-TO-CONVEXITY, SPIRALLIKENESS AND $-LIKENESS IN THE UNIT DISC 63
2.4.1 CLOSE-TO-CONVEXITY IN THE UNIT DISC 63 2.4.2 SPIRALLIKE FUNCTIONS
IN THE UNIT DISC 73 2.4.3 $-LIKE FUNCTIONS ON THE UNIT DISC 79 3 THE
LOEWNER THEORY 87 3.1 LOEWNER CHAINS AND THE LOEWNER DIFFERENTIAL
EQUATION 87 3.1.1 KERNEL CONVERGENCE 87 3.1.2 SUBORDINATION CHAINS AND
KERNEL CONVERGENCE 94 3.1.3 LOEWNER S DIFFERENTIAL EQUATION 100 3.1.4
REMARKS ON BIEBERBACH S CONJECTURE 112 3.2 APPLICATIONS OF LOEWNER S
DIFFERENTIAL EQUATION TO THE STUDY OF UNIVALENT FUNCTIONS 117 3.2.1 THE
RADIUS OF STARLIKENESS FOR THE CLASS S AND THE ROTATION THEOREM 118
3.2.2 APPLICATIONS OF THE METHOD OF LOEWNER CHAINS TO CHARACTERIZE SOME
SUBCLASSES OF 5 126 3.3 UNIVALENCE CRITERIA 130 3.3.1 BECKER S
UNIVALENCE CRITERIA 130 3.3.2 UNIVALENCE CRITERIA INVOLVING THE
SCHWARZIAN DERIVATIVE . 132 3.3.3 A GENERALIZATION OF BECKER S AND
NEHARI S UNIVALENCE CRI- TERIA 140 4 BLOCH FUNCTIONS AND THE BLOCH
CONSTANT 145 4.1 PRELIMINARIES CONCERNING BLOCH FUNCTIONS 145 4.2 -THE
BLOCH CONSTANT PROBLEM AND BONK S DISTORTION THEOREM . . 151 4.3 LOCALLY
UNIVALENT BLOCH FUNCTIONS 157 4.3.1 DISTORTION RESULTS FOR LOCALLY
UNIVALENT BLOCH FUNCTIONS . 157 4.3.2 THE CASE OF CONVEX FUNCTIONS 163 5
LINEAR INVARIANCE IN THE UNIT DISC 165 5.1 GENERAL IDEAS CONCERNING
LINEAR-INVARIANT FAMILIES 165 5.2 EXTREMAL PROBLEMS AND RADIUS OF
UNIVALENCE 172 CONTENTS IX 5.2.1 BOUNDS FOR COEFFICIENTS OF FUNCTIONS IN
LINEAR-INVARIANT FAMILIES 172 5.2.2 RADIUS PROBLEMS FOR LINEAR-INVARIANT
FAMILIES 174 II UNIVALENT MAPPINGS IN SEVERAL COMPLEX VARIABLES AND
COMPLEX BANACH SPACES 181 6 UNIVALENCE IN SEVERAL COMPLEX VARIABLES 183
6.1 PRELIMINARIES CONCERNING HOLOMORPHIC MAPPINGS IN C * AND COM- PLEX
BANACH SPACES 184 6.1.1 HOLOMORPHIC FUNCTIONS IN C 184 6.1.2 CLASSES OF
DOMAINS IN C*. PSEUDOCONVEXITY 188 6.1.3 HOLOMORPHIC MAPPINGS 191 6.1.4
AUTOMORPHISMS OF THE EUCLIDEAN UNIT BALL AND THE UNIT POLYDISC 195 6.1.5
HOLOMORPHIC MAPPINGS IN COMPLEX BANACH SPACES . . . 197 6.1.6
GENERALIZATIONS OF FUNCTIONS WITH POSITIVE REAL PART . . . 202 6.1.7
EXAMPLES AND COUNTEREXAMPLES 210 6.2 CRITERIA FOR STARLIKENESS 213 6.2.1
CRITERIA FOR STARLIKENESS ON THE UNIT BALL IN C OR IN A COMPLEX BANACH
SPACE 213 6.2.2 STARLIKENESS CRITERIA ON MORE GENERAL DOMAINS IN C . .
217 6.2.3 SUFFICIENT CONDITIONS FOR STARLIKENESS FOR MAPPINGS OF CLASS C
1 219 6.2.4 STARLIKENESS OF ORDER 7 IN C 221 6.3 CRITERIA FOR CONVEXITY
223 6.3.1 CRITERIA FOR CONVEXITY ON THE UNIT POLYDISC AND THE EUCLIDEAN
UNIT BALL 223 6.3.2 NECESSARY AND SUFFICIENT CONDITIONS FOR CONVEXITY IN
COM- PLEX BANACH SPACES 230 6.3.3 QUASI-CONVEX MAPPINGS ON THE UNIT BALL
OF C 238 6.4 SPIRALLIKENESS AND ^-LIKENESS IN SEVERAL COMPLEX VARIABLES
. . . 244 X CONTENTS 7 GROWTH, COVERING AND DISTORTION RESULTS FOR
STARLIKE AND CONVEX MAPPINGS IN C * AND COMPLEX BANACH SPACES 255 7.1
GROWTH, COVERING AND DISTORTION RESULTS FOR STARLIKE MAPPINGS IN SEVERAL
COMPLEX VARIABLES AND COMPLEX BANACH SPACES 256 7.1.1 GROWTH AND
COVERING RESULTS FOR STARLIKE MAPPINGS ON THE UNIT BALL AND SOME
PSEUDOCONVEX DOMAINS IN C*. EXTENSIONS TO COMPLEX BANACH SPACES 256
7.1.2 BOUNDS FOR COEFFICIENTS OF NORMALIZED STARLIKE MAPPINGS IN C 262
7.1.3 A DISTORTION RESULT FOR A SUBCLASS OF STARLIKE MAPPINGS IN C 268
7.2 GROWTH, COVERING AND DISTORTION RESULTS FOR CONVEX MAPPINGS IN
SEVERAL COMPLEX VARIABLES AND COMPLEX BANACH SPACES 271 7.2.1 GROWTH AND
COVERING RESULTS FOR CONVEX MAPPINGS .... 271 7.2.2 COVERING THEOREM AND
THE TRANSLATION THEOREM IN THE CASE OF NONUNIVALENT CONVEX MAPPINGS IN
SEVERAL COMPLEX VARIABLES 278 7.2.3 BOUNDS FOR COEFFICIENTS OF CONVEX
MAPPINGS IN C 1 AND COMPLEX HILBERT SPACES 281 7.2.4 DISTORTION RESULTS
FOR CONVEX MAPPINGS IN C 1 AND COM- PLEX HILBERT SPACES 286 8 LOEWNER
CHAINS IN SEVERAL COMPLEX VARIABLES 295 8.1 LOEWNER CHAINS AND THE
LOEWNER DIFFERENTIAL EQUATION IN SEVERAL COMPLEX VARIABLES 295 8.1.1 THE
LOEWNER DIFFERENTIAL EQUATION IN C * 295 8.1.2 TRANSITION MAPPINGS
ASSOCIATED TO LOEWNER CHAINS ON THE UNIT BALL OF C 312 8.2
CLOSE-TO-STARLIKE AND SPIRALLIKE MAPPINGS OF TYPE ALPHA ON THE UNIT BALL
OF C 1 322 8.2.1 AN ALTERNATIVE CHARACTERIZATION OF SPIRALLIKENESS OF
TYPE ALPHA IN TERMS OF LOEWNER CHAINS 322 8.2.2 CLOSE-TO-STARLIKE
MAPPINGS ON THE UNIT BALL OF C* .... 324 CONTENTS XI 8.3 UNIVALENT
MAPPINGS WHICH ADMIT A PARAMETRIC REPRESENTATION . 330 8.3.1 EXAMPLES OF
MAPPINGS WHICH ADMIT PARAMETRIC REPRE- SENTATION ON THE UNIT BALL OF C *
330 8.3.2 GROWTH RESULTS AND COEFFICIENT BOUNDS FOR MAPPINGS IN S{B)
334 8.4 APPLICATIONS OF THE METHOD OF LOEWNER CHAINS TO UNIVALENCE
CRITERIA ON THE UNIT BALL OF C 348 8.5 LOEWNER CHAINS AND
QUASICONFORMAL EXTENSIONS OF HOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX
VARIABLES 353 8.5.1 CONSTRUCTION OF QUASICONFORMAL EXTENSIONS BY MEANS
OF LOEWNER CHAINS 353 8.5.2 STRONGLY STARLIKE AND STRONGLY SPIRALLIKE
MAPPINGS OF TYPE A ON THE UNIT BALL OF C 370 9 BLOCH CONSTANT PROBLEMS
IN SEVERAL COMPLEX VARIABLES 377 9.1 PRELIMINARIES AND A GENERALIZATION
OF BONK S DISTORTION THEOREM 377 9.2 BLOCH CONSTANTS FOR BOUNDED AND
QUASIREGULAR HOLOMORPHIC MAPPINGS 384 9.3 BLOCH CONSTANTS FOR STARLIKE
AND CONVEX MAPPINGS IN SEVERAL COMPLEX VARIABLES 390 10 LINEAR
INVARIANCE IN SEVERAL COMPLEX VARIABLES 395 10.1 PRELIMINARIES
CONCERNING THE NOTION OF LINEAR INVARIANCE IN SEV- ERAL COMPLEX
VARIABLES 396 10.1.1 L.I.F. S AND TRACE ORDER IN SEVERAL COMPLEX
VARIABLES . . 396 10.1.2 EXAMPLES OF L.I.F. S ON THE EUCLIDEAN UNIT BALL
OF C . 399 10.2 DISTORTION RESULTS FOR LINEAR-INVARIANT FAMILIES IN
SEVERAL COMPLEX VARIABLES 401 10.2.1 DISTORTION RESULTS FOR L.I.F. S ON
THE EUCLIDEAN UNIT BALL OF C 401 10.2.2 DISTORTION RESULTS FOR
L.I.F. S ON THE UNIT POLYDISC OF C 1 410 10.3 EXAMPLES OF L.I.F. S OF
MINIMUM ORDER ON THE EUCLIDEAN UNIT BALL AND THE UNIT POLYDISC OF C 414
XII CONTENTS 10.3.1 EXAMPLES OF L.I.F. S OF MINIMUM ORDER ON THE
EUCLIDEAN UNIT BALL OF C 414 10.3.2 EXAMPLES OF L.I.F. S OF MINIMUM
ORDER ON THE UNIT POLY- DISC OF C 426 10.4 NORM ORDER OF
LINEAR-INVARIANT FAMILIES IN SEVERAL COMPLEX VARI- ABLES 429 10.5 NORM
ORDER AND UNIVALENCE ON THE EUCLIDEAN UNIT BALL OF C . . 434 10.6
LINEAR-INVARIANT FAMINES IN COMPLEX HILBERT SPACES 440 11 UNIVALENT
MAPPINGS AND THE ROPER-SUFFRIDGE EXTENSION OPERATOR 443 11.1 CONVEX,
STARLIKE AND BLOCH MAPPINGS AND THE ROPER-SUFFRIDGE EXTENSION OPERATOR
444 11.2 GROWTH AND COVERING THEOREMS ASSOCIATED WITH THE ROPER-
SUFFRIDGE EXTENSION OPERATOR 456 11.3 LOEWNER CHAINS AND THE OPERATOR $
N ,A 461 11.4 RADIUS PROBLEMS AND THE OPERATOR $ N Q 466 11.5
LINEAR-INVARIANT FAMILIES AND THE OPERATOR $*, * 469 BIBLIOGRAPHY 477
LIST OF SYMBOLS 521 INDEX 527
|
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| indexdate | 2024-07-09T19:16:49Z |
| institution | BVB |
| isbn | 0824709764 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010450589 |
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| physical | XV, 530 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Dekker |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Graham, Ian Verfasser aut Geometric function theory in one and higher dimensions Ian Graham ; Gabriela Kohr New York [u.a.] Dekker 2003 XV, 530 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 255 Fonctions de plusieurs variables complexes Fonctions univalentes Fonctions, Théorie géométrique des Functions of several complex variables Geometric function theory Univalent functions Geometrische Funktionentheorie (DE-588)4156711-0 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 s DE-604 Kohr, Gabriela Verfasser aut Pure and applied mathematics 255 (DE-604)BV000001885 255 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010450589&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Graham, Ian Kohr, Gabriela Geometric function theory in one and higher dimensions Pure and applied mathematics Fonctions de plusieurs variables complexes Fonctions univalentes Fonctions, Théorie géométrique des Functions of several complex variables Geometric function theory Univalent functions Geometrische Funktionentheorie (DE-588)4156711-0 gnd |
| subject_GND | (DE-588)4156711-0 |
| title | Geometric function theory in one and higher dimensions |
| title_auth | Geometric function theory in one and higher dimensions |
| title_exact_search | Geometric function theory in one and higher dimensions |
| title_full | Geometric function theory in one and higher dimensions Ian Graham ; Gabriela Kohr |
| title_fullStr | Geometric function theory in one and higher dimensions Ian Graham ; Gabriela Kohr |
| title_full_unstemmed | Geometric function theory in one and higher dimensions Ian Graham ; Gabriela Kohr |
| title_short | Geometric function theory in one and higher dimensions |
| title_sort | geometric function theory in one and higher dimensions |
| topic | Fonctions de plusieurs variables complexes Fonctions univalentes Fonctions, Théorie géométrique des Functions of several complex variables Geometric function theory Univalent functions Geometrische Funktionentheorie (DE-588)4156711-0 gnd |
| topic_facet | Fonctions de plusieurs variables complexes Fonctions univalentes Fonctions, Théorie géométrique des Functions of several complex variables Geometric function theory Univalent functions Geometrische Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010450589&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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