Geodesic
Representing systems of exponentials in projective limits of weighted subspaces of $H(D)$
Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 232-250

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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. 
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     author = {K. P. Isaev and K. V. Trounov and R. S. Yulmukhametov},
     title = {Representing systems of exponentials in projective limits of weighted subspaces of $H(D)$},
     journal = {Izvestiya. Mathematics },
     pages = {232--250},
     publisher = {mathdoc},
     volume = {83},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a3/}
}
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K. P. Isaev; K. V. Trounov; R. S. Yulmukhametov. Representing systems of exponentials in projective limits of weighted subspaces of $H(D)$. Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 232-250. http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a3/