## Realizability Theory for Continuous Linear SystemsConcise exposition of realizability theory as applied to continous linear systems, specifically to the operators generated by physical systems as mappings of stimuli into responses. Many problems included. |

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### Contents

VectorValued Functions | 1 |

1ntegration with VectorValued Functions | 23 |

BanachSpaceValued Testing Functions | 49 |

Kernel Operators | 77 |

Convolution Operators | 96 |

The Laplave Transformation | 118 |

Analyticity and the Exchange Formula | 119 |

The Admittance Formulism | 149 |

Appendix A Linear Spaces | 194 |

Appendix E 1nductiveLimit Spaces | 211 |

Appendix F Bilinear Mappings and Tensor Products | 213 |

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1n view 1ndeed 1t follows a e H analytic function Appendix assume B]-valued Banach space Bochner integral Borel subsets bounded set called causal choose compact interval compact set complex-valued continuous function continuous linear mapping converges convolution operator defined definition denote dense distributions equation exists a unique fixed Frechet space given Hence Hilbert port Hilbert space hounded implies inductive-limit inequality integer k e integral Jm(A kernel operator Laplace transform Lemma Let f linear space linear translation-invariant locally convex space lossless Moreover neighborhood nonnegative integer norm notation obtain open set positive measure Problem product topology PROOF properties representation respect result right-hand side satisfies scatter-passive Section seminorms semipassive separately continuous sequence sesquilinear form simple functions SSVar strong operator topology subspace supp tends to zero testing-function space Theorem theory uniquely determined valued function Zemanian