Arbitrarily slow rational approximations on the positive real line

Rational Approximation on the Positive Real Axis

Introduction Rational Chebyshev approximation to reciprocals of certain entire functions by reciprocals of polynomials on the positive real axis has recently attracted the attention of many mathematicians . By developing certain new methods of approach we successfully attacked ([3]-[6]) some of the related problems . This paper is a continuation of our earlier papers ([3]-[6] ) . The results of...

Orthogonal rational functions and quadrature on the real half line

In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Padé approximant...

Pie ewise Rational Approximations of Real Algebrai Curves

Constrained Nonsmooth Utility Maximization on the Positive Real Line

We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor’s portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their dual relationship. We simplify the present proofs in this area and extend th...

On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by . An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here. © 2007 Elsevier B.V. All rights reserved.