Two applications of the subnormality of the Hessenberg matrix related to general orthogonal polynomials |
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| Authors: | V. Tomeo E. Torrano |
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| Affiliation: | a Escuela de Estad?´stica, Univ. Complutense de Madrid, Avda. de la Ciudad Universitaria s/n, 28040 Madrid, Spain
b Dept. Mat. Aplicada, Facultad de Informática, Univ. Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain |
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| Abstract: | In this paper we prove two consequences of the subnormal character of the Hessenberg matrix D when the hermitian matrix M of an inner product is a moment matrix. If this inner product is defined by a measure supported on an algebraic curve in the complex plane, then D satisfies the equation of the curve in a noncommutative sense. We also prove an extension of the Krein theorem for discrete measures on the complex plane based on properties of subnormal operators. |
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| Keywords: | 42C05 15A09 47B20 |
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