This paper investigates the construction of an optimal quadrature formula for Fourier integrals of ????(????) function using the method of ????-functions. The function ????(????) belongs to the Hilbert space, which consists of absolutely continuous functions with quadratically integrable first-order derivatives. We explore the problem of optimality in the sense of Sard, aiming to minimize the supremum of the absolute error |????????(????)| over all functions in. The method of ????-functions provides a means to derive the coefficients ???????? that achieve this minimal error. Our work details the ????-function method and its application to constructing optimal quadrature formulas, presenting a systematic approach to minimizing the quadrature error.
| Mualliflar | Abduakhadov, A.A., Абдуахадов, A.A. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2025-01-03 |
| Son | 4/2 |
| Betlar | 108-117 |
| Til | Ingliz |
Hilbert space, phi-function method, the optimal quadrature formula, error of the quadrature formula, Гильбертово пространство, метод фи-функций, оптимальная квадратурная формула, погрешность формулы
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