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 semi- integer degree. Also, we consider the Christoffel function, and prove that it satisfies extremal property analogous with the algebraic case.
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