A. M. Dilmukhametova, A. U. Mullabaeva, V. V. Napalkov, “Generalized Fock space”, Ufimsk. Mat. Zh., 2010, Volume 2, Issue 1,Pages <nobr>52

This article is cited in 4 papers

Generalized Fock space

A. M. Dilmukhametova^a, A. U. Mullabaeva^a, V. V. Napalkov^b

^a Bashkir State University, Ufa, Russia
^b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: We introduce a generalized Fock space and consider main properties of this space. There is found an adjoint operation to operation of multiplication on variable $z$. Also there are defined eigenfunctions of adjoint operator. We study a generalized Laplace transformation and problem of construction of basis for introduced space.

Keywords: the Fock space, an adjoint operator, the Laplace transformation, basis of the space, order and type of entire functions, the generalized differential operator.

UDC: 517.5

Received: 18.02.2010