Orthogonal Homogeneous Polynomials

AbstractAn addition formula, Pythagorean identity, and generating function are obtained for orthogonal homogeneous polynomials of several real variables. Application is made to the study of series of such polynomials. Results include an analog of the Funk-Hecke theorem

The Operator Fejér-Riesz Theorem

The Fejér-Riesz theorem has inspired numerous generalizations in one and several variables, and for matrix- and operator-valued functions. This paper is a survey of some old and recent topics that center around Rosenblum’s operator generalization of the classical Fejér-Riesz theorem