Asymptotics for Stieltjes polynomials,padé-type approximants,and Gauss-Kronrod quadrature

We study the asymptotic properties of Stieltjes polynomials outside the support of the measure as well as the asymptotic behaviour of their zeros. These properties are used to estimate the rate of convergence of sequences of rational functions, whose poles are partially fixed, which approximate Markovtype functions. An estimate for the speed of convergence of the Gauss-Kronrod quadrature formula in the case of analytic functions is also given.     

An optimal<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-bound on the Krein spectral shift function

Let ξ_A,B be the Krein spectral shift function for a pair of operatorsA, B, with C =A-B trace class. We establish the bound

A Class of Multiderivative Hybrid One-step Methods

This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximations to function exp(q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s 1 free parameters. The order of the algorithms satisfies s 1≤p≤2s 2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.     

Magnetic bottles for the Neumann problem: The case of dimension 3

The main object of this paper is to analyze the recent results obtained on the Neumann realization of the Schrödinger operator in the case of dimension 3 by Lu and Pan. After presenting a short treatment of their spectral analysis of keymodels, we show briefly how to implement the techniques of Helffer-Morame in order to give some localization of the ground state. This leaves open the question of the localization by curvature effect which was solved in the case of dimension 2 in our previous work and will be analysed in the case of dimension 3 in a future paper.