Evenly positive definite function of Hilbert space and some algebraic relationship

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.

Keywords

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