## Symmetric Hilbert Spaces and Related Topics: Infinitely Divisible Positive Definite Functions. Continuous Products and Tensor Products. Gaussian and Poissonian Stochastic Processes |

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### Contents

Introduction | vii |

The symmetric Hilbert space of a Hilbert space | 18 |

Positive definite functions of type S | 30 |

Copyright | |

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1-cocycle bijective Boolean algebra Borel structure Borel subset called carrying character of G coboundary cocycle complex numbers conditionally positive definite consider continuous positive definite continuous product continuous tensor product converges countable define denote disjoint element example exists a unique exp(i f in F fact factorizable finite partition finite positive finite subset Fourier transform function f Gaussian measure hermitian Hilbert space Im(b implies infinitely divisible integrable isomorphism k.EXP kernel lemma Let G linear process linear subspace locally compact group measure space moreover multiplication operator negligible notations null orthogonal orthonormal basis positive definite function positive measure probability space proof Proposition prove quadratic form Radon measure real function representation of G restricted product satisfying scalar product space H standard Borel space suppose symmetric Hilbert spaces theorem tion topological unique isomorphism unitary operator vector space