Real, complex and functional analysis

The error estimates of minimal and almost minimal cubature formulas on classes of periodic functions

V. L. Vaskevich<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: A power-law order of convergence to zero of a sequence of norms of error functionals for minimal and almost minimal cubature formulas is established. Functionals act on multidimensional periodic Sobolev spaces, including on spaces with fractional smoothness.

Keywords: cubature formulas, minimal and almost minimal cubature formulas, the convergence order, error functionals, extremal functions, embedding constants.

UDC: 517.518.23

MSC: 65D32

Received August 28, 2018, published October 5, 2018

DOI: 10.17377/semi.2018.15.090

Bibliographic databases:

•