About a system of anti-periodic trigonometric functions

作者：Berriochoa E; Cachafeiro A^*; Garcia Amor J

来源：Computers & Mathematics with Applications, 2008, 56(6): 1526-1537.

DOI：10.1016/j.camwa.2008.03.005

• trigonometric orthogonal functions
• bi-orthogonality
• orthogonal polynomials on the unit circle
• recurrence relations
• Verblunsky parameters

In this paper we introduce the so-called second kind trigonometric system, which is a useful tool for the representation of 2 pi "anti-periodic" functions. Using these functions we study a sequence of trigonometric polynomials, which are bi-orthogonal in the Szego's sense. We study the usual topics in the theory of Fourier series and we present a new connection with the orthogonal polynomials (OP) on the unit circle and some useful properties like: recurrence relations, kernel representations and a Favard's type theorem.

• 出版日期2008-9