Rational Approximation and its Applications in Mathematics Physics

A survey of bounds for the zeros of analytic functions obtained by continued fraction methods.- Rational approximation and interpolation of functions by branched continued fractions.- Polynomial condition of Leja.- Branched continued fractions and convergence acceleration problems.- Two-point Padé-type and Padé Approximants.- Existence of Chebyshev approximations by transformations of powered rationals.- Best Chebyshev rational approximants and poles of functions.- Hyperbolic approximation of meromorphic functions.- Three different approaches to a proof of convergence for Padé approximants.- On the continuity properties of the multivariate Padé-Operator T m,n .- The Marchaud inequality for generalized Moduli of smoothness.- Analytic properties of two-dimensional continued P-fraction expansions with periodical coefficients and their simultaneous Pade-Hermite approximants.- Modification of generalised continued fractions I definition and application to the limit-periodic case.- Convergence acceleration for continued fractions K(an/1), where an ? ?.- Perron-Carathéodory continued fractions.- On approximation of functions by two-dimensional continued fractions.- On the convergence of the multidimensional limit-periodic continued fractions.- Quelques generalisations de la representation de reels par des fractions continues.- Local properties of continued fractions.- A Stieltjes analysis of the K+-p forward elastic amplitude.- Smoothness conditions for Stieltjes measures from Pade approximants.- Exact multisoliton properties of rational approximants to the iterated solution of nonlinear evolution equations.- Application of rational approximations to some functional equations.- Operator rational functions and variational methods for the model operator.- Thegeneralized Schur algorithm for the superfast solution of Toeplitz systems.- Strong unicity in nonlinear approximation.