Shell polynomials and indeterminate moment problems
نویسندگان
چکیده
منابع مشابه
A question by T. S. Chihara about shell polynomials and indeterminate moment problems
The generalized Stieltjes–Wigert polynomials depending on parameters 0 ≤ p < 1 and 0 < q < 1 are discussed. By removing the mass at zero of an N-extremal solution concentrated in the zeros of the D-function from the Nevanlinna parametrization, we obtain a discrete measure μM , which is uniquely determined by its moments. We calculate the coefficients of the corresponding orthonormal polynomials...
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For an indeterminate moment problem we denote the orthonormal polynomials by Pn. We study the relation between the growth of the function P (z) = ( ∑∞ n=0 |Pn(z)|) and summability properties of the sequence (Pn(z)). Under certain assumptions on the recurrence coefficients from the three term recurrence relation zPn(z) = bnPn+1(z) + anPn(z) + bn−1Pn−1(z), we show that the function P is of order ...
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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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For a class of orthogonal polynomials related to the q-Meixner polynomials corresponding to an indeterminate moment problem we give a one-parameter family of orthogonality measures. For these measures we complement the orthogonal polynomials to an orthogonal basis for the corresponding weighted L-space explicitly. The result is proved in two ways; by a spectral decomposition of a suitable opera...
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This paper deals with the indeterminate moment problem on the real line. We are given a positive measure μ on R having moments of all orders and we assume that μ is not determined by its moments. For details about the indeterminate moment problem see the monographs by Akhiezer, by Shohat and Tamarkin or the survey paper by Berg. Our notation follows that of Akhiezer. In this indeterminate situa...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00715-9