Quadrature on the half line and two-point Pade approximants to Stieltjes functions. Part III. The unbounded case

[摘要] Let alpha be a general, absolutely continuous measure, possibly complex, supported on [0, infinity). Let F-alpha(z) denote its Cauchy transform. In this paper we prove, under suitable conditions, the convergence of two-point Pade type approximants to F-alpha and of the associated quadrature formulas Sigma(j=1)(n) A(j)f(x(j)) to the integral integral(0)(infinity) f(x)d alpha(x). These quadrature formulas can be of Gaussian or of interpolatory type. Estimates for the rate of convergence are also included.

[发布日期] 1997-12-18

[关键词] two-point Pade approximation;Stieltjes function;orthogonal Laurent polynomials;quadrature formula