l h e problem of approximating a high order controller by a low order one is tackled with the aid of a frequency-weighted Hankel norm approximation procedure. Bounds are obtained which weight those arising in the unweighted Hankel norm approximation procedure by a factor depending solely on the weighting function. Keywards. Controllers; approximation theory; controller reduction; system order r...

In [I], a method was given for optimal Hankel-norm approximation with frequency weighting. In a broad sense, this method stands in the same relation to frequency-weighted balanced approximation [2] as unweighted optimal Hankel-norm approximation stands in relation to unweighted balanced approximation, see, e.g. [3]. No bounds were given in [I] on the frequency-domain error associated with frequ...

In this article, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $L^{2}(Sigma)$ such as, $n$-power normal, $n$-power quasi-normal, $k$-quasi-paranormal and quasi-class$A$. Then we show that weighted composition operators can separate these classes.

‎In this paper, we provide a complete description of weighted composition operators between extended Lipschitz algebras on compact metric spaces. We give necessary and sufficient conditions for the injectivity and the sujectivity of these operators. We also obtain some sufficient conditions and some necessary conditions for a weighted composition operator between these spaces to be compact.

These are the notes of the lecture course given at LTCC in 2015. The aim of the course is to consider the following three classes of operators: Toeplitz and Hankel operators on the Hardy space on the unit circle and Toeplitz operators on the Bergman space on the unit disk. For each of these three classes of operators, we consider the following questions: boundedness and estimates or explicit ex...