Abstract
The extremum problem for the Wiener–Hopf equation obtained by replacing the condition u(x) = 0, x < 0, by the condition of the minimum of the quadratic functional of the function u(x)exp(−x), −∞ < x < ∞, is solved in closed form.
Similar content being viewed by others
REFERENCES
V. M. Alekseev, É. M. Galeev, and V. M. Tikhomirov, Selected Optimization Problems [in Russian], Nauka, Moscow (1984).
E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals [Russian translation], Gostekhizdat, Moscow-Leningrad (1948).
F. D. Gakhov and Yu. I. Cherskii, Equations of the Convolution Type [in Russian], Nauka, Moscow (1978).
M. G. Krein, “Integral equations on a half-line with kernels dependent on the difference of arguments,” Usp. Mat. Nauk, 13, No.5, 3–120 (1958).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cherskii, Y.I. Extremum Problem for the Wiener–Hopf Equation. Ukrainian Mathematical Journal 52, 1310–1314 (2000). https://doi.org/10.1023/A:1010369508209
Issue Date:
DOI: https://doi.org/10.1023/A:1010369508209