## One-Parameter Semigroups for Linear Evolution EquationsThis book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background. |

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### Contents

III | 4 |

Strongly Continuous Semigroups | 36 |

Notes | 46 |

Semigroups Everywhere | 347 |

A Brief History of the Exponential Function | 497 |

Appendix | 509 |

Epilogue | 531 |

References | 555 |

List of Symbols and Abbreviations | 577 |

### Other editions - View all

One-Parameter Semigroups for Linear Evolution Equations Klaus-Jochen Engel,Rainer Nagel Limited preview - 2006 |

One-Parameter Semigroups for Linear Evolution Equations Klaus-Jochen Engel,Rainer Nagel No preview available - 2013 |

One-Parameter Semigroups for Linear Evolution Equations Klaus-Jochen Engel,Rainer Nagel No preview available - 2014 |

### Common terms and phrases

A G p(A abstract Cauchy problem adjoint algebra analytic semigroup approximate assume assumption Banach space bounded operator characterization compact operator continuous functions contraction semigroup converges Corollary Deﬁnition denote densely deﬁned differential equation differential operator domain D(A eigenvalue estimate Example Exercise exists exponential function ﬁnd ﬁrst following assertions formula function q functional equation functional equation FE G D(A G L(X growth bound hence Hilbert space Hint implies integral inverse Lemma linear operator Math matrix Moreover multiplication operator multiplication semigroup norm continuous obtain one-parameter operator Mq operator topology operators T(t Paragraph perturbation PROOF Proposition prove result satisﬁes satisfying Section semi semigroup T(t))t20 sequence Sobolev space solution spectral bound spectral mapping theorem spectral theory spectrum strong operator topology strongly continuous semigroup subspace theory translation semigroup unbounded uniformly continuous WSMT