Multivariable approximate Carleman-type theorems for complex measures

We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for quasi-analytic functions of several variables. As an application, we obtain a discrete Phragm\'{e}n--Lindel\"{o}f-type theorem for analytic functions on ${\mathbb{C}}_+^n$.Comment: Published at http://dx.doi.org/10.1214/009117906000000377 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Weighted multiple interpolation and the control of perturbed semigroup systems

In this paper the controllabillity and admissibility of perturbed semigroup systems are studied, using tools from the theory of interpolation and Carleson measures. In addition, there are new results on the perturbation of Carleson measures and on the weighted interpolation of functions and their derivatives in Hardy spaces, which are of interest in their own right

Robust identification in H∞

AbstractWe consider system identification in the Banach space H∞ in the framework proposed by Helmicki, Jacobson, and Nett. It is shown that there is no robustly convergent linear algorithm for identifying exponentially stable systems in the presence of noise which is not tuned to prior information about the unknown system or noise. Various nonlinear algorithms, some closely related to one of Gu and Khargonekar, are analysed, and results on trigonometric interpolation used to provide new error bounds. An application of these techniques to approximation is given, and finally some numerical results are provided for illustration

The group of invariants of an inner function with finite spectrum

This paper determines the group of continuous invariants corresponding to an inner function $\Theta$ with finitely many singularities on the unit circle $T$; that is, the continuous mappings $g: T \to T$ such that $\Theta \circ g = \Theta$ on \T. These mappings form a group under composition.Comment: 14 pages, 3 figures, submitted for publication May 201