M. G. Krein's ideas in the theory of orthogonal polynomials
Mark Grigorievich Krein surely made various relevant contributions to the theory of orthogonal polynomials, starting with his investigations of the spectra of Jacobi matrices in the problem of harmonic oscillations of certain mechanical systems. Some of Krein's contributions are sketched in this paper. Among them are Krein's theorem which characterizes orthogonal polynomials on the real line with a measure supported on a set with a finite number of accumulation points, Krein's initiation of matrix and operator moment problems, Krein's contribution to the extension of Szegö's theorem for orthogonal polynomials on the unit circle, and finally Krein's complete description of the zeros of orthogonal polynomials on the unit circle with an indefinite weight.
scientific article; zbMATH DE number 803819
scientific article