Geodesic
Representing Systems of Exponentials in Weight Subspaces $H(D)$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 13-28

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In this paper, weight subspaces of the space of analytic functions on a bounded convex domain of the complex plane are considered. Descriptions of spaces that are strongly conjugate to inductive and projective limits of uniformly weight spaces of analytic functions in a bounded convex domain $D\subset \mathbb C$ are obtained in terms of the Fourier–Laplace transformation. For each normed uniformly weight space $H(D,u)$, the smallest linear space $\mathcal H_i(D,u)$ that contains $H(D,u)$ and is invariant under differentiation and the largest linear space $\mathcal H_p(D,u)$ that is contained in $H(D,u)$ and is invariant under differentiation are constructed. Natural locally convex topologies are introduced on these spaces and a description of strongly conjugate spaces in terms of the Fourier–Laplace transformation is presented. The existence of representing exponential systems in the space $\mathcal H_i(D,u)$ is proved.
Keywords: analytic functions, integer functions, series of exponentials, sufficient sets. 
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     author = {R. A. Bashmakov and K. P. Isaev and R. S. Yulmukhametov},
     title = {Representing {Systems} of {Exponentials} in {Weight} {Subspaces} $H(D)$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {13--28},
     publisher = {mathdoc},
     volume = {153},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_153_a1/}
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R. A. Bashmakov; K. P. Isaev; R. S. Yulmukhametov. Representing Systems of Exponentials in Weight Subspaces $H(D)$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 13-28. http://geodesic.mathdoc.fr/item/INTO_2018_153_a1/