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Classification of $E_0$-Semigroups by Product Systems

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In these notes the author presents a complete theory of classification of $E_0$-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.

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Machine Name: SAXO081