139 research outputs found
On the class SI of J-contractive functions intertwining solutions of linear differential equations
In the PhD thesis of the second author under the supervision of the third
author was defined the class SI of J-contractive functions, depending on a
parameter and arising as transfer functions of overdetermined conservative 2D
systems invariant in one direction. In this paper we extend and solve in the
class SI, a number of problems originally set for the class SC of functions
contractive in the open right-half plane, and unitary on the imaginary line
with respect to some preassigned signature matrix J. The problems we consider
include the Schur algorithm, the partial realization problem and the
Nevanlinna-Pick interpolation problem. The arguments rely on a correspondence
between elements in a given subclass of SI and elements in SC. Another
important tool in the arguments is a new result pertaining to the classical
tangential Schur algorithm.Comment: 46 page
The Transformation of Issai Schur and Related Topics in an Indefinite Setting
We review our recent work on the Schur transformation for scalar generalized Schur and Nevanlinna functions. The Schur transformation is defined for these classes of functions in several situations, and it is used to solve corresponding basic interpolation problems and problems of factorization of rational J-unitary matrix functions into elementary factors. A key role is played by the theory of reproducing kernel Pontryagin spaces and linear relations in these spaces
Kernel-based Active Subspaces with application to CFD parametric problems using Discontinuous Galerkin method
A new method to perform a nonlinear reduction in parameter spaces is
proposed. By using a kernel approach it is possible to find active subspaces in
high-dimensional feature spaces. A mathematical foundation of the method is
presented, with several applications to benchmark model functions, both scalar
and vector-valued. We also apply the kernel-based active subspaces extension to
a CFD parametric problem using the Discontinuous Galerkin method. A full
comparison with respect to the linear active subspaces technique is provided
for all the applications, proving the better performances of the proposed
method. Moreover we show how the new kernel method overcomes the drawbacks of
the active subspaces application for radial symmetric model functions
Superoscillations and Analytic Extension in Schur Analysis
We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of Rfunctions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results
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