Matrix-valued orthogonal polynomials on the real line: some extensions of the classical theory
L Miranian · Journal of Physics A Mathematical and General · 2005
In the work presented below the classical subject of orthogonal polynomials on the real line is discussed in the matrix setting. An analogue of the determinant definition of orthogonal polynomials is presented; the classical properties such as the recurrence relation, the kernel polynomials, and the Christoffel–Darboux formula are discussed. A τ-function for the system of matrix-valued orthogonal polynomials on the real line is presented. Some properties of the τ-functions are investigated.