## Abstract

Consider a semigroup T on a Banach space X and a (possibly unbounded) operator C densely defined in X, with values in another Banach space. We give some necessary as well as some sufficient conditions for C to be an admissible observation operator for T, i.e., any finite segment of the output function y(t)=C T_{ t} x, t≧0, should be in L^{ p} and should depend continuously on the initial state x. Our approach is to start from a description of the map which takes initial states into output functions in terms of a functional equation. We also introduce an extension of C which permits a pointwise interpretation of y(t)=C T_{ t} x, even if the trajectory of x is not in the domain of C.

Original language | English |
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Pages (from-to) | 17-43 |

Number of pages | 27 |

Journal | Israel Journal of Mathematics |

Volume | 65 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1989 |

Externally published | Yes |