On the Carleson measure criterion in linear systems theory

Bernhard H. Haak (1)

1 IMB - Institut de Mathématiques de Bordeaux

In Ho, Russell, and Weiss, a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given. We extend their results from the Hilbert space situation $X=\ell_2$ and $L^2$--admissibility to the more general situation of $L^p$--admissibility on $\ell_q$--spaces. In case of analytic diagonal semigroups we present a new result that does not rely on Laplace transform methods. A comparison of both criteria leads to result of $L^p$--admissibility for reciprocal systems in the sense of Curtain.

Domaines: Optimisation et contrôle [math.OC]; Variables complexes [math.CV]

Bernhard H. Haak. On the Carleson measure criterion in linear systems theory. Complex Analysis and Operator Theory, 2008, pp.1-19. ⟨hal-00274320v2⟩