Quadrature rules of Gaussian type for trigonometric polynomials with preassigned nodes (Q6546961)

The paper deals with quadrature rules of Gaussian type for trigonometric polynomials with preassigned nodes. In Section 1 (Introduction), the authors recall some notions regarding the trigonometric polynomials and the degree of exactness for Gaussian type quadratures for these polynomials. Section 2 is devoted to quadrature rules of Gaussian type for trigonometric polynomials with preassigned nodes. The main result of this section is Theorem 2.1, where necessary and sufficient conditions for a quadrature rule to be of Gaussian type are given. In Section 3, the authors discuss the optimal set of quadrature rules for trigonometric polynomials with preassigned nodes, the main result of the Section being Theorem 3.1. Finally, some numerical examples are presented.