Geodesic
Interpolation by series of exponential functions whose exponents are condensed in a certain direction
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 62-79

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For complex interpolation nodes, we study the problem of interpolation by series of exponential functions whose exponents form a set, which is condensed at infinity in a certain direction. We obtain a criterion for all sets of nodes from a special class. For arbitrary sets of nodes, we obtain a necessary condition for the solvability of a more general problem of interpolation by functions that can be represented as Radon integrals of an exponential function over a set of exponents. The paper also contains well-known results on interpolation, which, in particular, allow studying the multipoint holomorphic Vallée Poussin problem for convolution operators.
Keywords: series of exponential functions, exponent of exponential function, limit direction of exponents, convolution operator, Cauchy problem, Radon integral.
Mots-clés : interpolation, Vallée Poussin problem 
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     author = {S. G. Merzlyakov and S. V. Popenov},
     title = {Interpolation by series of exponential functions whose exponents are condensed in a certain direction},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {62--79},
     publisher = {mathdoc},
     volume = {162},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2019_162_a6/}
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S. G. Merzlyakov; S. V. Popenov. Interpolation by series of exponential functions whose exponents are condensed in a certain direction. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 62-79. http://geodesic.mathdoc.fr/item/INTO_2019_162_a6/