caa a22 4500 46793164X CHVBK 20180406152945.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s00020-005-1416-y doi (NATIONALLICENCE)springer-10.1007/s00020-005-1416-y Admissibility of Unbounded Operators and Wellposedness of Linear Systems in Banach Spaces [Elektronische Daten] [Bernhard Haak, Peer Kunstmann] Abstract.: We study linear systems, described by operators A, B, C for which the state space X is a Banach space.We suppose that −A generates a bounded analytic semigroup and give conditions for admissibility of B and C corresponding to those in G. Weiss' conjecture. The crucial assumptions on A are boundedness of an H∞-calculus or suitable square function estimates, allowing to use techniques recently developed by N. Kalton and L. Weis. For observation spaces Y or control spaces U that are not Hilbert spaces we are led to a notion of admissibility extending previous considerations by C. Le Merdy. We also obtain a characterisation of wellposedness for the full system. We give several examples for admissible operators including point observation and point control. At the end we study a heat equation in X = Lp(Ω),1<p< ∞, with boundary observation and control and prove its wellposedness for several function spaces Y and U on the boundary ∂Ω. Birkhäuser Verlag, Basel, 2005 Control theory nationallicence linear systems nationallicence admissibility nationallicence H ∞-calculus nationallicence squarefunction estimates nationallicence Haak Bernhard Mathematisches Institut I, Universität Karlsruhe, Englerstraße 2, D-76128, Karlsruhe, Germany aut Kunstmann Peer Mathematisches Institut I, Universität Karlsruhe, Englerstraße 2, D-76128, Karlsruhe, Germany aut Integral Equations and Operator Theory Birkhäuser-Verlag; http://www.birkhauser.ch 55/4(2006-08-01), 497-533 0378-620X 55:4<497 2006 55 20 https://doi.org/10.1007/s00020-005-1416-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1416-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Haak Bernhard Mathematisches Institut I, Universität Karlsruhe, Englerstraße 2, D-76128, Karlsruhe, Germany aut NATIONALLICENCE 700 1- Kunstmann Peer Mathematisches Institut I, Universität Karlsruhe, Englerstraße 2, D-76128, Karlsruhe, Germany aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; http://www.birkhauser.ch 55/4(2006-08-01), 497-533 0378-620X 55:4<497 2006 55 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer