Abstract
New criteria for nonnegativity of connection coeffi- cients between to systems of orthogonal polynomials are given. The results apply to classical orthogonal polynomials. n X m=0 c(n,m)qm. The numbers c(n,m) are called the connection coeffcients from P to Q. Many problems in harmonic analysis related to nontrigonometric or- thogonal expansions depend on nonnegativity of connection coefficients (see (2, Lecture 7), (5)). Also nonnegativity of connection coefficients from a given system of orthogonal polynomials P to Tchebyshev poly- nomials (so-called property T) was used in (9) to derive nonnegativity of linearization of the system P. Property T was used in (10) in proving central limit theorems related to random walks associated with P. There are a few criterion for nonnegativity of connection coefficents. Some of them are given in terms of corresponding spectral measures
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