The central role of Montel's theorem in complex function theory

We begin with some new characterizations of normal families. Then we shift gears to see that normal families lie at the basis of complex function theory. Whereas normal families are usually treated as an ancillary topic in complex function theory, we show here that many of the main ideas in the subj...

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Vydáno v:Complex variables and elliptic equations Ročník 70; číslo 9; s. 1615 - 1625
Hlavní autoři: Krantz, Steven G., Dovbush, Peter V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Colchester Taylor & Francis 02.09.2025
Taylor & Francis Ltd
Témata:
holomorphic functions of several complex variables
Marty's criterion
normal families
Schottky's theorem
Theorems
ISSN:1747-6933, 1747-6941
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Shrnutí:We begin with some new characterizations of normal families. Then we shift gears to see that normal families lie at the basis of complex function theory. Whereas normal families are usually treated as an ancillary topic in complex function theory, we show here that many of the main ideas in the subject may be derived from Montel's theorem. Several consequences are derived.
Bibliografie:ObjectType-Article-1
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ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2024.2417344