Normal families and normal functions:
"This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
2024
|
| Ausgabe: | First edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis zbMATH |
| Zusammenfassung: | "This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations. The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions. This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples. The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts"-- |
| Beschreibung: | Includes bibliographical references and index Literaturverzeichnis: Seite 235-258 |
| Beschreibung: | viii, 260 Seiten |
| ISBN: | 9781032666365 9781032669878 |
Internformat
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| 245 | 1 | 0 | |a Normal families and normal functions |c Peter V. Dovbush and Steven G. Krantz |
| 250 | |a First edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2024 | |
| 300 | |a viii, 260 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 500 | |a Literaturverzeichnis: Seite 235-258 | ||
| 505 | 8 | |a Introduction -- A glimpse of normal families -- Normal families in C[superscript n] -- Normal functions in C[superscript n] -- A geometric approach to the theory of normal families -- Some classical theorems -- Normal families of holomorphic functions -- Spaces that omit the values 0 and 1 -- Concluding remarks. | |
| 520 | 3 | |a "This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations. The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions. This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples. The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts"-- | |
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Datensatz im Suchindex
| _version_ | 1825744082061754369 |
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| adam_text | |
| any_adam_object | |
| author | Dovbush, Peter V. Krantz, Steven G. 1951- |
| author_GND | (DE-588)130535907 |
| author_facet | Dovbush, Peter V. Krantz, Steven G. 1951- |
| author_role | aut aut |
| author_sort | Dovbush, Peter V. |
| author_variant | p v d pv pvd s g k sg sgk |
| building | Verbundindex |
| bvnumber | BV050191464 |
| contents | Introduction -- A glimpse of normal families -- Normal families in C[superscript n] -- Normal functions in C[superscript n] -- A geometric approach to the theory of normal families -- Some classical theorems -- Normal families of holomorphic functions -- Spaces that omit the values 0 and 1 -- Concluding remarks. |
| ctrlnum | (DE-599)KXP1871519233 |
| dewey-full | 515/.98 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.98 |
| dewey-search | 515/.98 |
| dewey-sort | 3515 298 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | First edition |
| format | Book |
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| id | DE-604.BV050191464 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-05T09:00:39Z |
| institution | BVB |
| isbn | 9781032666365 9781032669878 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035526995 |
| open_access_boolean | |
| owner | DE-20 |
| owner_facet | DE-20 |
| physical | viii, 260 Seiten |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Dovbush, Peter V. Verfasser aut Normal families and normal functions Peter V. Dovbush and Steven G. Krantz First edition Boca Raton ; London ; New York CRC Press 2024 viii, 260 Seiten txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Literaturverzeichnis: Seite 235-258 Introduction -- A glimpse of normal families -- Normal families in C[superscript n] -- Normal functions in C[superscript n] -- A geometric approach to the theory of normal families -- Some classical theorems -- Normal families of holomorphic functions -- Spaces that omit the values 0 and 1 -- Concluding remarks. "This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations. The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions. This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples. The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts"-- Lindelöf-Prinzip (DE-588)1347525602 gnd rswk-swf Normale Familie Mathematik (DE-588)4316944-2 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Holomorphe Funktion (DE-588)4025645-5 gnd rswk-swf Meromorphe Funktion (DE-588)4136862-9 gnd rswk-swf Holomorphic functions Functions, Meromorphic Normale Familie Mathematik (DE-588)4316944-2 s Holomorphe Funktion (DE-588)4025645-5 s Meromorphe Funktion (DE-588)4136862-9 s Mehrere komplexe Variable (DE-588)4169285-8 s Lindelöf-Prinzip (DE-588)1347525602 s DE-604 Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut 10.1201/9781032669861 9781032669861 ebook Erscheint auch als Online-Ausgabe 9781032669861 B:DE-89 V:DE-601 pdf/application https://www.gbv.de/dms/tib-ub-hannover/1871519233.pdf 2024-11-24 Inhaltsverzeichnis https://zbmath.org/7875846 zbMATH |
| spellingShingle | Dovbush, Peter V. Krantz, Steven G. 1951- Normal families and normal functions Introduction -- A glimpse of normal families -- Normal families in C[superscript n] -- Normal functions in C[superscript n] -- A geometric approach to the theory of normal families -- Some classical theorems -- Normal families of holomorphic functions -- Spaces that omit the values 0 and 1 -- Concluding remarks. Lindelöf-Prinzip (DE-588)1347525602 gnd Normale Familie Mathematik (DE-588)4316944-2 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Meromorphe Funktion (DE-588)4136862-9 gnd |
| subject_GND | (DE-588)1347525602 (DE-588)4316944-2 (DE-588)4169285-8 (DE-588)4025645-5 (DE-588)4136862-9 |
| title | Normal families and normal functions |
| title_auth | Normal families and normal functions |
| title_exact_search | Normal families and normal functions |
| title_full | Normal families and normal functions Peter V. Dovbush and Steven G. Krantz |
| title_fullStr | Normal families and normal functions Peter V. Dovbush and Steven G. Krantz |
| title_full_unstemmed | Normal families and normal functions Peter V. Dovbush and Steven G. Krantz |
| title_short | Normal families and normal functions |
| title_sort | normal families and normal functions |
| topic | Lindelöf-Prinzip (DE-588)1347525602 gnd Normale Familie Mathematik (DE-588)4316944-2 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Holomorphe Funktion (DE-588)4025645-5 gnd Meromorphe Funktion (DE-588)4136862-9 gnd |
| topic_facet | Lindelöf-Prinzip Normale Familie Mathematik Mehrere komplexe Variable Holomorphe Funktion Meromorphe Funktion |
| url | https://www.gbv.de/dms/tib-ub-hannover/1871519233.pdf https://zbmath.org/7875846 |
| work_keys_str_mv | AT dovbushpeterv normalfamiliesandnormalfunctions AT krantzsteveng normalfamiliesandnormalfunctions |