Geodesic
On a functional equation with holomorphic coefficients associated with a finite group
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2023), pp. 3-9

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{We consider a convex pentagon $D$ that has a pair of parallel and equal sides without a common vertex. We study the linear difference equation associated with this polygon. The coefficients of the equation and the free term are holomorphic in $D$. The solution is sought in the class of functions holomorphic outside the "half" of the $\partial D$ boundary and vanishing at infinity. A method for its regularization is proposed and a condition for its equivalence is found. The solution is represented as a Cauchy-type integral with an unknown density. The principle of contraction mappings in a Banach space is essentially used. Applications to interpolation problems for entire functions of exponential type are indicated.
Keywords: regularization method, Carleman boundary value problem, interpolation problems for entire functions. 
@article{IVM_2023_8_a0,
     author = {F. N. Garif'yanov and E. V. Strezhneva},
     title = {On a functional equation with holomorphic coefficients associated with a finite group},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--9},
     publisher = {mathdoc},
     number = {8},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_8_a0/}
}
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F. N. Garif'yanov; E. V. Strezhneva. On a functional equation with holomorphic coefficients associated with a finite group. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2023), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2023_8_a0/