Journal ArticleDOI
On the four-element equation for the functions analytic beyond a trapezoid and its applications
F. N. Garif’yanov,S. A. Modina +1 more
TLDR
In this paper, the four-element linear functional equation is studied in the class of functions analytic beyond an isosceles trapezoid and vanishing at infinity, where a system of entire functions is constructed of completely regular growth biorthogonal with a piecewise exponential weight to the system of powers on the coordinate axis.Abstract:
The four-element linear functional equation is studied in the class of functions analytic beyond an isosceles trapezoid and vanishing at infinity. Some system of entire functions is constructed of completely regular growth biorthogonal with a piecewise exponential weight to the system of powers on the coordinate axis.read more
Citations
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Sum-difference equation for analytic functions generated by pentagon and its application
E. P. Aksenteva,F. N. Garifyanov +1 more
TL;DR: For analytic functions, this paper studied poly-element linear functional equation generated by a pentagon and connected it with the moment problem for entire functions of exponential type, and showed that such equations are connected with the moments problem for all analytic functions.
Journal ArticleDOI
Summary equation for functions analytical outside a quadrangle
TL;DR: In this article, a linear four-element functional equation is considered and its solutions are holomorphic outside of a quadrangle and vanish at the infinity point, and a system of entire functions of completely regular growth, which is bi-orthogonal on three rays with piecewise exponential weight to the system of powers.
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Multielement equations for analytic functions in the plane with cuts
TL;DR: In this paper, the authors consider linear equations for analytic functions in the complex plane with cuts along a half of the boundary of a quadrangle and propose a regularization method that reduces the equations to an equation with summary-difference kernels.
Journal ArticleDOI
On Summary Equation Generated by a Quadrangle
TL;DR: In this article, the authors investigated a four-element functional equation in a class of solutions holomorphic outside a quadrangle and vanishing at infinity and proposed equivalent regularization method of such quadrangles.
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Regularization of a Class of Summary Equations
TL;DR: In this paper, a four-element linear summary equation is considered and a solution is sought in the form of the Cauchy type integral over an arbitrary quadrangle with unknown density.
References
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Journal ArticleDOI
Convolution equations in multidimensional spaces
TL;DR: The dissertation was defended on Nov. 10, 1977, at the session of the Specialized Council D 002.38.03 at the V. Steklov Mathematics Institute of the Academy of Sciences of the USSR.
Journal ArticleDOI
Stieltjes Moments of Entire Functions of Exponential Type
TL;DR: The lacunary homogeneous moment problem in the class of entire functions of exponential type is studied in this paper, where the authors consider the case of functions of the exponential type.