Оптимизация приближенного вычисления интегралов от быстроосцилирующих функций в пространстве Соболева комплекснозначных функций

Integrals of rapidly oscillating functions arise mainly in the theory of special functions and Fourier analysis, but also in other applied and computational sciences and engineering, for example, in theoretical physics, acoustic scattering, quantum chemistry, transport theory, electromagnetism, telecommunications, mechanics, and so on.The computation of integrals of rapidly oscillating functions is often carried out using the Filon method. The Filon method resembles Simpson’s quadrature formula. However, whereas in Simpson’s method the entire integrand is approximated by a parabola, in the Filon method only the function f(x) is approximated by a parabola. In this way, Filon derived a quadrature formula with coefficients that depend onw. In this work, optimal quadrature formulas in the Sobolev space of complex-valued periodic functions will be constructed for the approximate computation of rapidly oscillating integrals.