A trigonometric orthogonality with respect to a nonnegative Borel measure

Abstract

In this paper we consider trigonometric polynomials of semi-integer degree orthogonal with respect to a linear functional, defined by a nonnegative Borel measure. By using a suitable vector form we consider the corresponding Fourier sums and reproducing kernels for trigonometric polynomials of semiinteger degree. Also, we consider the Christoffel function, and prove that it satisfies extremal property analogous with the algebraic case.