报告地点：行健楼学术活动室526
邀请人：黄益副教授
摘要：
W. Hahn stated and solved the following interesting problem: to describe all families of polynomials orthogonal on the real line, whose derivatives themselves are orthogonal on the real line with respect to another positive weight. The solution consists of the three classical families of orthogonal polynomials named after Jacobi, Laguerre and Hermite. Ya. L. Geronimus solved this problem in its general form: he replaced the integral with respect to a positive weight to a general (non-degenerate in a certain sense) functional of orthogonality. As a result, the full solution turns to include one additional family known as Bessel polynomials (also, the parameters of the classical weights allow non-standard values). As a tool Geronimus stated and solved another interesting problem: which condition arise, when orthogonal polynomials of one family may be expressed as linear combinations of a finite number of polynomials of another family. In this talk we shall discuss certain extensions of these problems – in particular, an adaptation of Geronumus’s results to multiple orthogonality.
