Hankel operators and best Hankel approximation on the half-plane

The objective of this paper is to give an interrelation between Hankel oeprators on the unit disc and Hankel operators on the half-plane. As an application, the AAK result on the half-plane is established and the rate of best Hankel approximation on the halfplane is derived.

[1]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[2]  Teiji Takagi,et al.  On an Algebraic Problem Reluted to an Analytic Theorem of Carathéodory and Fejér and on an Allied Theorem of Landau , 1924 .

[3]  J. Partington An introduction to Hankel operators , 1988 .

[4]  C. Carathéodory,et al.  Über den zusammenhang der extremen von harmonischen funktionen mit ihren koeffizienten und über den picard-landau’schen satz , 1911 .

[5]  J. Schur,et al.  Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. , 1917 .

[6]  Z. Nehari On Bounded Bilinear Forms , 1957 .

[7]  S. Kung,et al.  Optimal Hankel-norm model reductions: Multivariable systems , 1980 .

[8]  Charles K. Chui,et al.  Rate of convergence of schmidt pairs and rational functions corresponding to best approximants of truncated hankel operators , 1992, Math. Control. Signals Syst..

[9]  M. Kreĭn,et al.  ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM , 1971 .

[10]  S. Power Hankel Operators on Hilbert Space , 1980 .

[11]  Sun-Yuan Kung,et al.  Optimal Hankel-norm model reductions-scalar systems , 1980 .

[12]  K. Glover All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[13]  Philip Hartman,et al.  On completely continuous Hankel matrices , 1958 .

[14]  M. Omizo,et al.  Modeling , 1983, Encyclopedic Dictionary of Archaeology.

[15]  Guanrong Chen,et al.  Signal Processing and Systems Theory: Selected Topics , 1992 .

[16]  M. Kreĭn,et al.  Introduction to the theory of linear nonselfadjoint operators , 1969 .

[17]  L. Trefethen,et al.  The CF table , 1990 .

[18]  Continuity of Best Hankel Approximation and Convergence of Near-BestApproximants , 1994 .

[19]  Ruth F. Curtain Proceedings of NATO Advanced Research Workshop on Modelling, robustness and sensitivity reduction in control systems , 1987 .

[20]  Ruth F. Curtain,et al.  Robust stabilization of infinite dimensional systems by finite dimensional controllers , 1986 .

[21]  Charles K. Chui,et al.  System reduction via truncated Hankel matrices , 1991, Math. Control. Signals Syst..