A trigonometric orthogonality with respect to a nonnegative Borel measure

作者：Milovanovic Gradimir V^*; Cvetkovic Aleksandar S; Stanic Marija P

来源：Filomat, 2012, 26(4): 689-696.

DOI：10.2298/FIL1204689M

• Trigonometric polynomial of semi-integer degree
• orthogonality
• nonnegative Borel measure
• Fourier series
• reproducing kernel
• Christoffel function

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.

• 出版日期2012-11