An elementary description of ideals localization methods
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 207-232
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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].
@article{ZNSL_1989_170_a11,
author = {N. K. Nikolskii},
title = {An elementary description of ideals localization methods},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {207--232},
publisher = {mathdoc},
volume = {170},
year = {1989},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a11/}
}
N. K. Nikolskii. An elementary description of ideals localization methods. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 207-232. http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a11/