# D. A. Mierzejewski

Search this author in Google Scholar

### The investigation of a generalized moment problem associated with correlation measures

Yu. M. Berezansky, D. A. Mierzejewski

Methods Funct. Anal. Topology **13** (2007), no. 2, 124-151

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).

### Generalized Jacobi fields

Methods Funct. Anal. Topology **9** (2003), no. 1, 80-100

### The structure of the extended symmetric Fock space

Yurij M. Berezansky, Dmytro A. Mierzejewski

Methods Funct. Anal. Topology **6** (2000), no. 4, 1-13