Evenly positive definite function of Hilbert space and some algebraic relationship

O. V. Lopotko

doi:10.30970/ms.55.1.85-93

O. V. Lopotko National Forestry and Wood Technology University of Ukraine

DOI: https://doi.org/10.30970/ms.55.1.85-93

Keywords: : integral representation; bounded evenly positive definite functions; bounded self-adjoint operators

Abstract

A generalization of P. A. Minlos, V. V. Sazonov’s theorem is proved in the case of bounded evenly positive definite function given in a Hilbert space. The integral representation is obtained for a family of bounded commutative self-adjoint operators which are connected by algebraic relationship.

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