# On the Carleson measure criterion in linear systems theory - Mathematics > Optimization and Control

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Abstract: In Ho, Russell, and Weiss, a Carleson measure criterion for admissibility ofone-dimensional input elements with respect to diagonal semigroups is given. Weextend 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 newresult that does not rely on Laplace transform methods. A comparison of bothcriteria leads to result of $L^p$-admissibility for reciprocal systems in thesense of Curtain.

Autor: Bernhard Hermann Haak IMB

Fuente: https://arxiv.org/