Realizability Theory for Continuous Linear Systems
Concise 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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1ntegration with VectorValued Functions
BanachSpaceValued Testing Functions
The Laplave Transformation
Analyticity and the Exchange Formula
The Admittance Formulism
Appendix A Linear Spaces
Appendix E 1nductiveLimit Spaces
Appendix F Bilinear Mappings and Tensor Products
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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