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On moment problem for entire functions generated by doubly periodic group

2020
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Ufimskii Matematicheskii Zhurnal
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We consider a lacunar problem for Stieltjes moments with an exponential weight. The solution is sought in the class of entire functions of exponential type, the indicator diagram of which is a some square. We construct nontrivial solutions of the corresponding homogeneous problem. This problem is reduced to the study of a linear total equation in the class of functions holomorphic outside four squares. At infinity, they have zero of a multiplicity at least three. Their boundary values satisfy

doi:10.13108/2020-12-2-21
fatcat:7w36diirdbepjjcxvlrltgiu5u