Hamburger Moment Problems and Orthogonal Polynomials
نویسندگان
چکیده
منابع مشابه
Hamburger Moment Problems and Orthogonal Polynomials
We consider a sequence of orthogonal polynomials given by the classical three term recurrence relation. We address the problem of deciding the determinacy or indeterminacy of the associated Hamburger moment problem on the basis of the behavior of the coefficients in the three term recurrence relation. Comparisons are made with other criteria in the literature. The efficacy of the criteria obtai...
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In 1894 Thomas Jan Stieltjes (1856-1894) published an extremely influential paper: Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse, 8, 1–122; 9, 5–47. He introduced what is now known as the Stieltjes integral with respect to an increasing function φ, the latter describing a distribution of mass (a measure μ) via the convention that the mass in an interval ]a, b] is μ(]a, b]) = φ...
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Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to the moment functional a finite set of mass points, or by multiplying it times a polynomial of total degree 2, respectively. Orthogonal polynomia...
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The recovering of a positive density, of which a nite number of moments is assigned, is considered (in the Stieltjes and Hamburger moment problems). In the choice of the approximant the Maximum Entropy approach is adopted. Two main problems are taken into account. 1. A review of diierent criteria concerning the determinacy and indeterminacy of the innnite moment problem is presented. This revie...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1989
ISSN: 0002-9947
DOI: 10.2307/2001379