Quasi-potential functions associated with orthogonal polynomials (Q1360761)

This is a survey on results on estimates of the partial sums of so-called quasipotential functions \(F(x,y;\lambda)\) associated with systems of orthogonal polynomials in \((-1,1)\) with respect to nonnegative finite Borel measures. If \(\{p_n\}^\infty_1\), \(\{q_n\}^\infty_1\) are such systems of orthogonal polynomials then \(F\) is defined by \(F(x,y;\lambda)= \sum^\infty_{k=0}\lambda_kp_k(x)q_k(y)\), \(\lambda_k\in\mathbb{R}\), \(k=0,1,\dots\)\ . Two theorems are formulated (without proof).