|
Zapiski Nauchnykh Seminarov LOMI, 1989, Volume 170, Pages 207–232
(Mi znsl4462)
|
|
|
|
This article is cited in 3 scientific papers (total in 3 papers)
An elementary description of ideals localization methods
N. K. Nikolskii
Abstract:
The paper is a short survey of a part of the theory of divisorial
ideals for algebras (and spaces) of holomorphlc functions
$X$ determined by growth conditions near the boundary:
$X=X(\{\lambda_n\})\stackrel{def}{=}\{\,f\in\mathrm{Hol}\,(\Omega): |f(z)|\leqslant c\lambda_n(z), z\in\Omega; c=c_f, n=n_f\,\}$
where $\Omega\subset\mathbb{C}$, $\lambda_n$ are positive in $\Omega$. All methods used to
prove divisoriality are classified into three groups: direct canonical
products method by Weieratrass and Hadamard; approximate
identity method by L. Schwartz and A. Beurling; spectral (resolvent,
with estimations) method by L. Waelbroeck, L. Hörmander et al.
Some observations and propositions seem to be new.
Formally speaking, the paper can be considered as part II of survey [1].
Citation:
N. K. Nikolskii, “An elementary description of ideals localization methods”, Investigations on linear operators and function theory. Part 17, Zap. Nauchn. Sem. LOMI, 170, "Nauka", Leningrad. Otdel., Leningrad, 1989, 207–232; J. Soviet Math., 63:2 (1993), 233–245
Linking options:
https://www.mathnet.ru/eng/znsl4462 https://www.mathnet.ru/eng/znsl/v170/p207
|
Statistics & downloads: |
Abstract page: | 185 | Full-text PDF : | 49 |
|