On the Carleson measure criterion in linear systems theory

Details On the Carleson measure criterion in linear systems theory On the Carleson measure criterion in linear systems theory

2008-04-18

arxiv.org/abs/0804.3000v2

Mathematics

Optimization and Control

to appear in Complex Analysis and Operator Theory

Scientific paper

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.

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