Resumen de Optimal cubature formulas related to tomography for certain classes of functions defined on a cube

Vladislav Babenko, Sergiy Borodachov, Dmytro Skorokhodov

• We study the problem of constructing an optimal cubature formula for approximate integration over the cube [0, 1]d . Our construction uses the information given by n integrals along intersections of [0, 1]d with shifts of coordinate subspaces of a given codimension k, 0 < k < d. We find a family of optimal formulas of this type for the class of functions defined on [0, 1]d which controls the modulus of continuity with respect to the max-norm in R d . When the majorant ω for the moduli of continuity of functions in the class is strictly increasing the family we find describes the set of all optimal cubature formulas.