Індекс рубрикатора НБУВ: В162.1

Рубрики:

Лінійні, лінійні нормовані і лінійні топологічні простори

Шифр НБУВ: Ж26161 Пошук видання у каталогах НБУВ 

We generalize the notion of a Jacobi field which is a family of operators with certain properties acting in the Fock space. Namely, we introduce a notion of generalized Jacobi field acting in a space more general than the Fock space. We discuss a particular case where this spectral measure is the Gamma measure and the operators of the field act in the so-called extended Fock space.

The classical power moment problem can be viewed as a theory of spectral representations of a positive functional on some classical commutative algebra with involution. We generalize this approach to the case where the algebra is a special commutative algebra of functions on the space of multiple finite configurations. If the above-mentioned functional is generated by a measure on the space of usual finite configurations then this measure is a correlation measure for a probability spectral measure on the space of infinite configurations. The latter measure is practically arbitrary, so that we have a connection between this complicated measure and its correlation measure defined on more simple objects that are finite configurations. The paper gives an answer to the following question: when this latter measure is a correlation measure for a complicated measure on infinite configurations? (Such measures are essential objects of statistical mechanics.)