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Mathematics of Control, Signals, and Systems

, 29:14

First Online: 15 June 2017Received: 16 June 2016Accepted: 29 May 2017DOI: 10.1007-s00498-017-0198-5

Cite this article as: Kucik, A.S. Math. Control Signals Syst. 2017 29: 14. doi:10.1007-s00498-017-0198-5


In this paper, we will establish necessary and sufficient conditions for a Laplace–Carleson embedding to be bounded for certain spaces of functions on the positive half-line. We will use these results to characterise weighted infinite-time admissibility of control and observation operators. We present examples of weighted admissibility criterion for one-dimensional heat equation with Neumann boundary conditions, and a cetrain parabolic diagonal system which was previously known to be not admissible in the unweighted setting.

KeywordsAdmissibility Besov spaces Carleson measure Laplace–Carleson embedding Laplace transform Linear evolution equation Semigroup system Mathematics Subject Classification30H20 30H25 47A57 93B28 

Author: Andrzej S. Kucik


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