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Papers by G. Lagomasino
Lecture Notes in Mathematics, 1984
Suppose a formal power series is given and that we know some facts about the (asymptotic) behavio... more Suppose a formal power series is given and that we know some facts about the (asymptotic) behavior of the poles (or part of them) for a certain subsequence of the associated Pad approximants. Inverse problems deal with finding out, with just this information, as much as possible about the analytical properties of the function corresponding to the power series. In the past two years, very important results have been obtained in this direction.
Sbornik: …, Jan 1, 2007
In this paper we study the approximability of the resolvent of an operator generated by a band ma... more In this paper we study the approximability of the resolvent of an operator generated by a band matrix by means of the resolvents of its finite-dimentional sections. For bounded perturbations of selfadjoint matrices a positive result in a large domain is obtained. We apply it to tridiagonal complex matrices in order to establish convergence conditions for Chebyshev continued fraction on sets of the complex domain. In the particular case of compact perturbation, this result is sharpened and the connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is shown. * Visiting Proffesor at Univ. Carlos
Journal of Approximation Theory, 1999
The concepts of definite and determinate Sobolev moment problem are introduced. The study of thes... more The concepts of definite and determinate Sobolev moment problem are introduced. The study of these questions is reduced to the definiteness or determinacy, respectively, of a system of classical moment problems by means of a canonical decomposition of the moment matrix associated with a Sobolev inner product in terms of Hankel matrices.
Constructive Approximation, 1995
The logarithmic asymptotics of Laurent-type orthogonal polynomials is obtained for a wide class o... more The logarithmic asymptotics of Laurent-type orthogonal polynomials is obtained for a wide class of weights. This is used to estimate the exact rate of convergence of two-point Padé approximants for the corresponding class of Stieltjes-type meromorphic functions.
Journal d'Analyse Mathématique, 1999
In this paper we obtain the strong asymptotics for the sequence of orthogonal polynomials with re... more In this paper we obtain the strong asymptotics for the sequence of orthogonal polynomials with respect to the inner product
Lecture Notes in Mathematics, 1984
Suppose a formal power series is given and that we know some facts about the (asymptotic) behavio... more Suppose a formal power series is given and that we know some facts about the (asymptotic) behavior of the poles (or part of them) for a certain subsequence of the associated Pad approximants. Inverse problems deal with finding out, with just this information, as much as possible about the analytical properties of the function corresponding to the power series. In the past two years, very important results have been obtained in this direction.
Sbornik: …, Jan 1, 2007
In this paper we study the approximability of the resolvent of an operator generated by a band ma... more In this paper we study the approximability of the resolvent of an operator generated by a band matrix by means of the resolvents of its finite-dimentional sections. For bounded perturbations of selfadjoint matrices a positive result in a large domain is obtained. We apply it to tridiagonal complex matrices in order to establish convergence conditions for Chebyshev continued fraction on sets of the complex domain. In the particular case of compact perturbation, this result is sharpened and the connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is shown. * Visiting Proffesor at Univ. Carlos
Journal of Approximation Theory, 1999
The concepts of definite and determinate Sobolev moment problem are introduced. The study of thes... more The concepts of definite and determinate Sobolev moment problem are introduced. The study of these questions is reduced to the definiteness or determinacy, respectively, of a system of classical moment problems by means of a canonical decomposition of the moment matrix associated with a Sobolev inner product in terms of Hankel matrices.
Constructive Approximation, 1995
The logarithmic asymptotics of Laurent-type orthogonal polynomials is obtained for a wide class o... more The logarithmic asymptotics of Laurent-type orthogonal polynomials is obtained for a wide class of weights. This is used to estimate the exact rate of convergence of two-point Padé approximants for the corresponding class of Stieltjes-type meromorphic functions.
Journal d'Analyse Mathématique, 1999
In this paper we obtain the strong asymptotics for the sequence of orthogonal polynomials with re... more In this paper we obtain the strong asymptotics for the sequence of orthogonal polynomials with respect to the inner product