Symmetric Hilbert Spaces and Related Topics: Infinitely Divisible Positive Definite Functions. Continuous Products and Tensor Products. Gaussian and Poissonian Stochastic Processes |
Contents
Introduction | 1 |
The symmetric Hilbert space of a Hilbert space | 18 |
Positive definite functions of type | 30 |
Copyright | |
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1-cocycle 6-algebra a₁ atomic b(gh bijection Boolean algebra Borel structure Borel subset called canonical carrying coboundary cocycle complex numbers conditionally positive definite consider continuous product continuous tensor product converges countable decomposable vectors define denote disjoint dv(t element example exists a unique exp(i factorizable finite partition finite positive finite subset Fock Fourier transform function f Gaussian measure Hilbert space implies infinitely divisible kernel L²(E L²(R lemma linear subspace locally compact group matrix measure space moreover morphism multiplication operator negligible null orthogonal orthonormal basis Poissonian positive definite function positive measure products of Hilbert proof properties Proposition prove quadratic form Radon measure restricted product satisfying space H standard Borel space subspace suppose theorem tion topology unique isomorphism unitary operator vector space von Neumann algebra write x₁