Search

We construct the Frobenius–Padé approximants of the function | x | in ( − 1 , 1 ) for the Chebyshev weight. These rational functions are linked with the Frobenius–Padé approximants of the function x in ( 0 , 1 ) . We prove geometric convergence of the approximants of | x | in C ∖ { z : ℜ ( z ) = 0 } . [ABSTRACT FROM AUTHOR]

Abstract: We obtain results on the convergence of Padé approximants of Stieltjes-type meromorphic functions and the relative asymptotics of orthogonal polynomials on unbounded intervals. These theorems extend some results given by Guillermo López in this direction substituting the Carleman condition in his theorems by the determination of the corresponding moment problem. [ABSTRACT FROM AUTHOR]

Abstract: For any pair of compact intervals of the real line , , with , we obtain two probability measures , , supported on and respectively, such that the Nikishin system has a sequence of monic multiple orthogonal polynomials which satisfy a four term recurrence relation with constant coefficients of period 2. The measures are obtained from the functions which give the ratio asymptotic of multiple orthogonal polynomials with respect to an arbitrary Nikishin system on , , such that a.e. on , . The role of , is symmetric in the sense that the same construction is possible on , , with . [ABSTRACT FROM AUTHOR]

Abstract: We obtain results on the convergence of Padé approximants of Stieltjes-type meromorphic functions and the relative asymptotics of orthogonal polynomials on unbounded intervals. These theorems extend some results given by Guillermo López in this direction substituting the Carleman condition in his theorems by the determination of the corresponding moment problem. [Copyright &y& Elsevier]

Abstract: We prove ratio asymptotic for sequences of multiple orthogonal polynomials with respect to a Nikishin system of measures such that for each k, has constant sign on its support consisting on an interval , on which almost everywhere, and a set without accumulation points in . [Copyright &y& Elsevier]

Abstract: Let be a finite positive Borel measure with compact support consisting of an interval plus a set of isolated points in , such that almost everywhere on . Let , be a sequence of polynomials, , with real coefficients whose zeros lie outside the smallest interval containing the support of . We prove ratio and relative asymptotics of sequences of orthogonal polynomials with respect to varying measures of the form . In particular, we obtain an analogue for varying measures of Denisov''s extension of Rakhmanov''s theorem on ratio asymptotics. These results on varying measures are applied to obtain ratio asymptotics for orthogonal polynomials with respect to fixed measures on the unit circle and for multi-orthogonal polynomials in which the measures involved are of the type described above. [Copyright &y& Elsevier]

Abstract: We study some properties of the zeros and the asymptotic behavior of orthogonal polynomials with respect to varying measures on the unit circle. In the proofs, some techniques of rational approximation are used. [Copyright &y& Elsevier]