Abstract
The moment problem and the investigation of the associated Jacobian matrices occupy an important place in the scientific heritage of M. Krein. This explains his natural interest in orthogonal polynomials. Although the number of Krein's works in this field is relatively small, his contribution to the theory of orthogonal polynomials is indeed fundamental. His ideas still have a significant influence on the researches of contemporary mathematicians as was indicated, in particular, by Professors Chihara, Dombrowski, Rodman, Van Assche, and others in their surw:y talks at the Conference "Orthogonal Polynomials and Their Applications" (1989, Columbus, USA).
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