153 research outputs found
On a Class of Functions Analytic in a Half-Disk and an Associated Interpolation Problem, Journal of Mathematical Analysis and Applications
In this paper we introduce a class of functions analytic in a half disk and for which the Nevanlinna-Pick interpolation problem has a solution in terms of a linear fractional transformation. The method used to solve this problem is that of the fundamental matrix inequality, suitably adapted to the present situation
On a Class of Functions Analytic in a Half-Disk and an Associated Interpolation Problem, Journal of Mathematical Analysis and Applications
In this paper we introduce a class of functions analytic in a half disk and for which the Nevanlinna-Pick interpolation problem has a solution in terms of a linear fractional transformation. The method used to solve this problem is that of the fundamental matrix inequality, suitably adapted to the present situation
Two-Sided Residue Interpolation in Matrix H2 Spaces With Symmetries: Conformal Conjugate Involutions
We consider two-sided and one-sided residue interpolation problem in classes of matrix-valued Hardy functions with various symmetries. These symmetries are defined in terms of conformal conjugate involutions of the unit disk. Problems with additional norm restrictions are studied as well. Applications are made to two-point interpolation
On Bitangential Interpolation in the Time Varying Setting for Hilbert-Schmidt Operators: The Continuous Case
The Hilbert space of lower triangular Hilbert–Schmidt operators on the real line is a natural analogue of the Hardy space of a half-plane, where the complex numbers are now replaced by matrix-valued functions. One can associate with a bounded operator its “values” at a matrix-valued function [see Ballet al.,Oper. Theory Adv. Appl.56(1992), 52–89], and this allows [see Ballet al.,Integral Equations Operator Theory20(1994), 1–43] to define and solve the analogue of the two-sided Nudelman interpolation problem for bounded operators (which form an analogue ofH∞(C+)). In this paper we consider the two-sided interpolation problem with a Hilbert–schmidt norm constraint (rather than the more common operator-norm constraint) on the interpolant
On Bitangential Interpolation in the Time Varying Setting for Hilbert-Schmidt Operators: The Continuous Case
The Hilbert space of lower triangular Hilbert–Schmidt operators on the real line is a natural analogue of the Hardy space of a half-plane, where the complex numbers are now replaced by matrix-valued functions. One can associate with a bounded operator its “values” at a matrix-valued function [see Ballet al.,Oper. Theory Adv. Appl.56(1992), 52–89], and this allows [see Ballet al.,Integral Equations Operator Theory20(1994), 1–43] to define and solve the analogue of the two-sided Nudelman interpolation problem for bounded operators (which form an analogue ofH∞(C+)). In this paper we consider the two-sided interpolation problem with a Hilbert–schmidt norm constraint (rather than the more common operator-norm constraint) on the interpolant
Bitangential interpolation in generalized Schur classes
Bitangential interpolation problems in the class of matrix valued functions
in the generalized Schur class are considered in both the open unit disc and
the open right half plane, including problems in which the solutions is not
assumed to be holomorphic at the interpolation points. Linear fractional
representations of the set of solutions to these problems are presented for
invertible and singular Hermitian Pick matrices. These representations make use
of a description of the ranges of linear fractional transformations with
suitably chosen domains that was developed in a previous paper.Comment: Second version, corrected typos, changed subsection 5.6, 47 page
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