Jackson inequality in \(L_{2}(\mathbb T^{N})\) with generalized modulus of continuity (Q643745)

After a special modulus of continuity is defined via a sequence of coefficients which are absolutely summable and sum to zero, approximation estimates are considered. Specifically, the error of approximation of \(2\pi\)-periodic, multivariate, square-integrable functions by approximants from linear combinations of exponentials whose complex powers are from a prescribed, fixed set is bounded above. These powers have to be multi-integer valued, so in particular the exponentials are also \(2\pi\)-periodic. In this set-up a Jackson-type error estimate is established.