|
This article is cited in 27 scientific papers (total in 28 papers)
Local description of closed ideals and submodules of analytic functions of one variable. I
I. F. Krasichkov-Ternovskii
Abstract:
Let $P$ be a topological module (over the ring of polynomials) of vector-valued functions $f\colon G\to\mathbf C^q$, holomorphic in a domain $G\subset\mathbf C$.
A closed submodule $I\subset P$ is local (that is, uniquely determined by the collection $I_\lambda$, $\lambda\in G$, of its localized submodules) if and only if $I$ is stable and saturated. A submodule is said to be stable if it admits division by binomials: $f\in I$, $\frac f{z-\lambda}\in I_\lambda\Rightarrow\frac f{z-\lambda}\in I$.
Being saturated amounts to possessing sufficiently many elements.
Bibliography: 26 titles.
Received: 20.12.1976
Citation:
I. F. Krasichkov-Ternovskii, “Local description of closed ideals and submodules of analytic functions of one variable. I”, Math. USSR-Izv., 14:1 (1980), 41–60
Linking options:
https://www.mathnet.ru/eng/im1578https://doi.org/10.1070/IM1980v014n01ABEH001070 https://www.mathnet.ru/eng/im/v43/i1/p44
|
Statistics & downloads: |
Abstract page: | 371 | Russian version PDF: | 116 | English version PDF: | 10 | References: | 55 | First page: | 2 |
|