Birkhoff Type 2-Periodic Trigonometric Interpolation in the Family of Trigonometric Polynomial

Abstract

A kind of Birkhoff type 2-periodic trigonometric interpolation problems with equidistant nodes for 2pi periodic functions is discussed in the family of trigonometric polynomial. We find the necessary and sufficient conditions for the solvable case of this interpolation problem. The expressions of the interpolation basis are constructed.