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 |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2025-01-03 |
| Son | 4/2 |
| Betlar | 108-117 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
Hilbert space, phi-function method, the optimal quadrature formula, error of the quadrature formula, Гильбертово пространство, метод фи-функций, оптимальная квадратурная формула, погрешность формулы
| APA | Abduakhadov, A.A., & Абдуахадов, A.A. (2025). Optimal Approximation of Fourier Integrals by the Phi-Function Method. Ҳисоблаш ва амалий математика муаммолари, (4/2), 108-117. https://journals.airi.uz/index.php/pvpm/article/view/68 |
|---|---|
| GOST (OAK) | Abduakhadov, A.A., Абдуахадов, A.A. Optimal Approximation of Fourier Integrals by the Phi-Function Method // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 4/2. – P. 108-117. |
| MLA | Abduakhadov, A.A., and Абдуахадов, A.A. “Optimal Approximation of Fourier Integrals by the Phi-Function Method.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 108-117, 2025. https://journals.airi.uz/index.php/pvpm/article/view/68 |
| Chicago | Abduakhadov, A.A., and Абдуахадов, A.A. “Optimal Approximation of Fourier Integrals by the Phi-Function Method.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 108-117 (2025). https://journals.airi.uz/index.php/pvpm/article/view/68 |
| Harvard | Abduakhadov, A.A., and Абдуахадов, A.A (2025) ‘Optimal Approximation of Fourier Integrals by the Phi-Function Method’, Ҳисоблаш ва амалий математика муаммолари, (4/2), 108-117. https://journals.airi.uz/index.php/pvpm/article/view/68 |
| BibTeX | @article{abduakhadovaa2025,
title = {Optimal Approximation of Fourier Integrals by the Phi-Function Method},
author = {Abduakhadov, A.A. and Абдуахадов, A.A.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {4/2},
pages = {108-117},
url = {https://journals.airi.uz/index.php/pvpm/article/view/68}
} |
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