Geodesic
Difference equation for functions analytical outside two squares
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 3-8

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We consider a totality of two squares constructed by primitive periods $1$ and $i$ and sufficiently close to each other. In a vicinity of this set we investigate four-element difference equation with constant coefficients, whose linear shifts are generating transforms of the corresponding doubly periodic group and the inverse transforms. We seek a solution in a class of functions analytical outside this set and vanishing at infinity. We indicate applications to the moments problem for entire functions of exponential type.
Keywords: difference equations, regularization method, moments problem. 
@article{IVM_2018_6_a0,
     author = {F. N. Garif'yanov and E. V. Strezhneva},
     title = {Difference equation for functions analytical outside two squares},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--8},
     publisher = {mathdoc},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_6_a0/}
}
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F. N. Garif'yanov; E. V. Strezhneva. Difference equation for functions analytical outside two squares. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2018), pp. 3-8. http://geodesic.mathdoc.fr/item/IVM_2018_6_a0/