Density of some systems of functions, quasianalyticity and subharmonic majorants
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 102-156
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This work is concerned with density of some rather common classes of entire functions (for example, with density of the class of all entire functions of order less than $\sigma$) in $\Phi$-spaces. One of the typical examples of а $\Phi$-space is $C(E)$, where $E$ is a closed subset of $\mathbb{R}$. The dual problems reduce to questions concerning the quasianalyticity of classes of functions with Fourier transforms supported on a thin set. The latter problems are treated as problems of potential theory. Conformal mappings of the upper-half plane to special "comb-like" domains are systematically used.
@article{ZNSL_1989_170_a7,
author = {B. Ya. Levin},
title = {Density of some systems of functions, quasianalyticity and subharmonic majorants},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {102--156},
publisher = {mathdoc},
volume = {170},
year = {1989},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a7/}
}
B. Ya. Levin. Density of some systems of functions, quasianalyticity and subharmonic majorants. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 102-156. http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a7/