The Experts below are selected from a list of 243 Experts worldwide ranked by ideXlab platform

Francesca Antoci - One of the best experts on this subject based on the ideXlab platform.

Vladimir Bolotnikov - One of the best experts on this subject based on the ideXlab platform.

  • realization and interpolation for schur agler class Functions on domains with matrix polynomial Defining Function in cn
    Journal of Functional Analysis, 2004
    Co-Authors: Joseph A Ball, Vladimir Bolotnikov
    Abstract:

    Abstract We consider a bitangential interpolation problem for operator-valued Functions defined on a general class of domains in C n (including as particular cases, Cartan domains of types I–III) which satisfy a type of von Neumann inequality associated with the domain. We show that any such Function has a realization in terms of a unitary colligation and the Defining polynomial for the domain. We show how the solution of various classes of bitangential interpolation problems for this class of Functions corresponds to a unitary extension of a particular partially defined isometry uniquely specified by the interpolation data. Criteria for existence of solutions are given (1) in terms of positivity of a certain kernel completely determined by the data, or, more generally, (2) by the existence of a positive-kernel solution of a certain generalized Stein equation completely determined by the data.

Anne-katrin Herbig - One of the best experts on this subject based on the ideXlab platform.

A K B Chand - One of the best experts on this subject based on the ideXlab platform.

  • A $\mathcal{C}^{1}$ -Rational Cubic Fractal Interpolation Function: Convergence and Associated Parameter Identification Problem
    Acta Applicandae Mathematicae, 2015
    Co-Authors: Pragasam Viswanathan, A K B Chand
    Abstract:

    This paper introduces a rational Fractal Interpolation Function (FIF), in the sense that it is obtained using a rational cubic spline transformation involving two shape parameters, and investigates its applicability in some constrained interpolation problems. We identify suitable values for the parameters of the corresponding Iterated Function System (IFS) so that it generates positive rational FIFs for a given set of positive data. Further, the problem of identifying the rational IFS parameters so as to ensure that its attractor (graph of the corresponding rational FIF) lies in a specified rectangle is also addressed. With the assumption that the data Defining Function is continuously differentiable, an upper bound for the interpolation error (with respect to the uniform norm) for the rational FIF is obtained. As a consequence, the uniform convergence of the rational FIF to the original Function as the norm of the partition tends to zero is proven.

  • a mathcal c 1 rational cubic fractal interpolation Function convergence and associated parameter identification problem
    Acta Applicandae Mathematicae, 2015
    Co-Authors: Pragasam Viswanathan, A K B Chand
    Abstract:

    This paper introduces a rational Fractal Interpolation Function (FIF), in the sense that it is obtained using a rational cubic spline transformation involving two shape parameters, and investigates its applicability in some constrained interpolation problems. We identify suitable values for the parameters of the corresponding Iterated Function System (IFS) so that it generates positive rational FIFs for a given set of positive data. Further, the problem of identifying the rational IFS parameters so as to ensure that its attractor (graph of the corresponding rational FIF) lies in a specified rectangle is also addressed. With the assumption that the data Defining Function is continuously differentiable, an upper bound for the interpolation error (with respect to the uniform norm) for the rational FIF is obtained. As a consequence, the uniform convergence of the rational FIF to the original Function as the norm of the partition tends to zero is proven.

Joseph A Ball - One of the best experts on this subject based on the ideXlab platform.

  • realization and interpolation for schur agler class Functions on domains with matrix polynomial Defining Function in cn
    Journal of Functional Analysis, 2004
    Co-Authors: Joseph A Ball, Vladimir Bolotnikov
    Abstract:

    Abstract We consider a bitangential interpolation problem for operator-valued Functions defined on a general class of domains in C n (including as particular cases, Cartan domains of types I–III) which satisfy a type of von Neumann inequality associated with the domain. We show that any such Function has a realization in terms of a unitary colligation and the Defining polynomial for the domain. We show how the solution of various classes of bitangential interpolation problems for this class of Functions corresponds to a unitary extension of a particular partially defined isometry uniquely specified by the interpolation data. Criteria for existence of solutions are given (1) in terms of positivity of a certain kernel completely determined by the data, or, more generally, (2) by the existence of a positive-kernel solution of a certain generalized Stein equation completely determined by the data.