Optimal Cubature Formulas on Classes of Periodic Functions in Several Variables
Bazarkhanov D.B.
March 2021Pleiades journals
Proceedings of the Steklov Institute of Mathematics
2021#312Issue 116 - 36 pp.
Abstract: We establish sharp order estimates for the error of optimal cubature formulas on the Nikol’skii–Besov and Lizorkin–Triebel type spaces, $$B^{s,mathtt{m}}_{p,q}(mathbb T^m)$$ and $$L^{s,mathtt{m}}_{p,q}(mathbb T^m)$$, respectively, for a number of relations between the parameters $$s$$, $$p$$, $$q$$, and $$mathtt{m}$$ ($$s=(s_1,dots,s_n)inmathbb R^n_+$$, $$1leq p,qleqinfty$$, $$mathtt{m}=(m_1,dots,m_n)in{mathbb N}^n$$, $$m=m_1+dots+m_n$$). Lower estimates are proved via Bakhvalov’s method. Upper estimates are based on Frolov’s cubature formulas.
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Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science of the Republic of Kazakhstan, Pushkina Str. 125, Almaty, 050010, Kazakhstan
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