منابع مشابه
On Higher Heine-stieltjes Polynomials
Take a linear ordinary differential operator d(z) = Pk i=1 Qi(z) d dzi with polynomial coefficients and set r = maxi=1,...,k(degQi(z) − i). If d(z) satisfies the conditions: i) r ≥ 0 and ii) degQk(z) = k + r we call it a nondegenerate higher Lamé operator. Following the classical examples of E. Heine and T. Stieltjes we initiated in [6] the study of the following multiparameter spectral problem...
متن کاملStieltjes-type Polynomials on the Unit Circle
Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carathéodory function. In turn, this is used to give an estimate of the rate of co...
متن کاملStieltjes-type polynomials on the unit circle
Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carathéodory function. In turn, this is used to give an estimate of the rate of co...
متن کاملOn Stieltjes Polynomials and Gauss-kronrod Quadrature
Let D be a real function such that D(z) is analytic and D(z) ± 0 for \z\ < 1. Furthermore, put W(x) = \J\ x2\D(e'v)\2 , x = costp , tp e [0, 71 ], and denote by pn(', rV) the polynomial which is orthogonal on [-1, +1] to Pn_[ (P„_! denotes the set of polynomials of degree at most n 1 ) with respect to W . In this paper it is shown that for each sufficiently large n the polynomial En+X(-, W) (ca...
متن کاملStieltjes polynomials and Lagrange interpolation
Bounds are proved for the Stieltjes polynomial En+1, and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. Applying these results, convergence theorems are proved for the Lagrange interpolation process...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1931
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1931-1501624-1