Exponentially weighted optimal quadrature formulas with complex exponential weights in the periodic Sobolev space ^ W (2,1,0) 2 (0,1]
##submission.downloads##
Ushbu maqola Sobolev fazosida
^
W
(2,1,0)
2
(0,1] davriy funksiyalar integrallarini yaqin hisoblash
uchun optimal kvadratur formulalarini qurishga bag‘ishlangan. Kvadratur formulalar murakkab
eksponensial og‘irlik funksiyasini e 2πiωx o‘z ichiga oladi. Formulalarning koeffitsiyentlari mos keluvchi
xatolik funksionalining konjugat fazodagi normasini minimallashtirish orqali aniqlanadi. Furye tahlili
va ekstremal funksiya usullaridan foydalanib, optimal koeffitsiyentlarning aniq ifodalari keltirib
chiqariladi. Ushbu natijalar kvadratur formulalarining klassik nazariyasini eksponensial og‘irlikli
va osillatsion hollarga kengaytiradi hamda davriy funksiyalarni sonli integrallash uchun samarali
sxemalarni beradi.
1. J.Ahlberg, E.Nilson, J.Walsh, The theory of splines and its application, Academic press Inc., New York.
2. S.L.Sobolev, The coefficients of optimal quadrature formulas, in: Selected Works of S.L.Sobolev. Springer,
pp. 561-566 (2006).
3. S.L.Sobolev, “Введение в теорию кубатурных формул”, Москва, издательство “Наука”.
4. Kh.M.Shadimetov, A.R.Hayotov, Construction of interpolation splines minimizing semi-norm in space.
Numerical mathematics 53(2). 2012
5. Shadimetov Kh.M., Azamov S.S. ,Kobilov H.M. Optimization of approximate integration formulas for
periodic function classes Problems of computational and applied mathematics no. 3(67) 2025
6. Azamov S.S., Qobilov H.M. Optimal quadrature formulas in the space of periodic functions journal of
International scientific journal of computing technologies and mathematical modeling
7. Hayotov A.R., Khayriev U.N, Makhkamova D. 2021. Optimal quadrature formula for approximate
calculation of integrals with exponential weight and its application. Bulletin of the Institute of
Mathematics, №2. Vol. 4. P. 99-108.
8. Shadimetov M.Kh. 2019. Optimal lattice quadrature and cubature formulas in Sobolev spaces. Monograph,
Ministry of Higher and Secondary Specialized Education of the Republic of Uzbekistan, Tashkent P. 97-
104. ISBN 978-9943-5958-2-8.
9. Shadimetov M.Kh. 1998. Weighted optimal quadrature formulas in a periodic Sobolev space. Uzbek Math.
Zh., №2. P. 76-86.
10. Sard A. 1949. Best approximate integration formulas; best approximation formulas, Amer. J. Math., №71.
P. 80-91.
Mulkiiyat (c) 2025 «O‘zMU XABARLARI»
Ushbu ish quyidagi litsenziya asosida ruxsatlangan Kreativ Commons Attribution-NonCommercial-ShareAlike 4.0 International litsenziyasi asosida bu ish ruxsatlangan..
.jpg)
.png)
