Geodesic
Representation of functions by series of exponents in normed subspaces of $A^\infty(D)$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 42-56

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We introduce the normalized space of functions that are analytic in a bounded convex domain and infinitely differentiable up to its boundary, with estimates of all derivatives determined by a logarithmically convex sequence of positive numbers. We prove that functions from this space are represented by series of exponents converging in a weakened norm. The main tool in the construction of systems of exponents are entire functions with a given asymptotic behavior. Also, a theorem on the joint approximation of subharmonic functions by the logarithms of the modules of entire functions is proved.
Keywords: analytic function, entire function, subharmonic function, series of exponents. 
@article{INTO_2019_162_a4,
     author = {K. P. Isaev and K. V. Trounov and R. S. Yulmukhametov},
     title = {Representation of functions by series of exponents in normed subspaces of $A^\infty(D)$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {42--56},
     publisher = {mathdoc},
     volume = {162},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_162_a4/}
}
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K. P. Isaev; K. V. Trounov; R. S. Yulmukhametov. Representation of functions by series of exponents in normed subspaces of $A^\infty(D)$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 42-56. http://geodesic.mathdoc.fr/item/INTO_2019_162_a4/