# Disproof of two conjectures of George Weiss

Jacob, B. and Zwart, H.J. (2000) *Disproof of two conjectures of George Weiss.* [Report]

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Abstract: | Two conjectures that were posed by Weiss almost ten years ago are shown not to hold. The first conjecture states that a scalar operator is admissible if and only a certain resolvent estimate holds. The second was posed by Weiss together with Russell and states that a system is exactly observable if and only if a test similar to the Hautus test for finite-dimensional systems holds. The -semigroup in both counter-examples is analytic and possesses a basis of eigenfunctions. |

Item Type: | Report |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/65733 |

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