On a Functional Equation with Holomorphic Coefficients Associated with a Finite Group.

Autor: Garif'yanov, F. N., Strezhneva, E. V.
Zdroj: Russian Mathematics; Aug2023, Vol. 67 Issue 8, p1-6, 6p
Abstrakt: We consider a convex pentagon 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 . The solution is sought in the class of functions holomorphic outside the "half" of the 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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