Generalized Hankel shifts and exact Jackson–Stechkin inequalities in L2
Обобщенные сдвиги Ганкеля и точные неравенства Джексона–Стечкина в L2
L2 метрикасындағы дәл Джексон–Стечкин теңсiздiктерi және жалпыланған Ганкелдiң ығыстыруы
Tileubayev T.E.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#110Issue 2142 - 149 pp.
In this paper, we have solved several extremal problems of the best mean-square approximation of functions f on the semiaxis with a power-law weight. In the Hilbert space L2 with a power-law weight t2α+1 we obtain Jackson–Stechkin type inequalities between the value of the Eσ(f)-best approximation of a function f(t) by partial Hankel integrals of an order not higher than σ over the Bessel functions of the first kind and the k-th order generalized modulus of smoothnes ωk(Brf,t), where B is a second–order differential operator.
best approximation , generalized modulus of smoothness of m-th order , Hilbert space
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
L.N. Gumilyov Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026