This article is cited in 3 papers

Representing systems of exponentials in projective limits of weighted subspaces of $H(D)$

K. P. Isaev^ab, K. V. Trounov^b, R. S. Yulmukhametov<sup>ab

a</sup> Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
^b Bashkir State University, Ufa

Abstract: We consider uniformly weighted spaces of analytic functions on a bounded convex domain in the complex plane with convex weights. For every uniformly weighted normed space $H(D,\varphi)$ we define a special inductive limit $\mathcal H_i(D,\varphi)$ of normed spaces and a special projective limit $\mathcal H_p(D,\varphi)$ of normed spaces. We prove that $\mathcal H_i(D,\varphi)$ is the smallest locally convex space which contains $H(D,\varphi)$ and is invariant under differentiation, and $\mathcal H_p(D,\varphi)$ is the largest such space which is contained in $H(D,\varphi)$. We construct a representing system of exponentials in the projective limit $\mathcal H_p(D, \varphi)$ and estimate the redundancy of this system.

Keywords: analytic functions, weighted spaces, locally convex spaces, sufficient sets, representing systems of exponentials.

UDC: 517.5

MSC: 30B50, 30H05, 30D15, 42A38, 46E10

Received: 27.10.2017
Revised: 17.07.2018

DOI: 10.4213/im8728

 English version: Izvestiya: Mathematics, 2019, 83:2, 232–250

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