Geodesic
On a difference equation with holomorphic coefficients generated by a hexagon
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2024), pp. 20-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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{Let $D$ be a hexagon with two straight and four right angles. We consider a seven-element difference equation with holomorphic coefficients generated by this hexagon. A method for regularizing this equation is proposed. The solution is sought in the class of functions holomorphic outside the "half" of the boundary $\partial D$ and vanishing at infinity. It is represented as a Cauchy-type integral over the "half" of the boundary with an unknown density. Applications to the problem of moments for entire functions of exponential type (e.f.e.t.) are indicated.
Keywords: multi-element functional equations, equivalent regularization method, moment problem for entire functions. 
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     author = {F. N. Garif'yanov and E. V. Strezhneva},
     title = {On a difference equation with holomorphic coefficients generated by a hexagon},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {20--26},
     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2024_8_a1/}
}
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F. N. Garif'yanov; E. V. Strezhneva. On a difference equation with holomorphic coefficients generated by a hexagon. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2024), pp. 20-26. http://geodesic.mathdoc.fr/item/IVM_2024_8_a1/

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