ON THE FORM OF CORRELATION
FUNCTION FOR A CLASS OF
NONSTATIONARY FIELD WITH
A ZERO SPECTRUM

RAE'D HATAMLEH

Abstract:

The present paper is devoted to the derivation of an explicit form of linearly representable random fields in the form $h(x_1, x_2)=\linebreak \exp{\{i(x_1A_1+x_2A_2)\}}h$, where $h\in H$, $H$ is a Hilbert space, operators $A_1,A_2$ are such that $A_1A_2=A_2A_1$ and $C^3=0$ where $%% C=A_1^*A_2-A_2A_1^*$. The results obtained are the generalization of theorem proved by Livshits and Yantsevitch [4] and Yantsevich and Abbaui [6]. It is shown that a rank of nonstationary of field $h(x_1,x_2)$ depends not only on a degree of nonself conjugation of $A_1,A_2$ but on a degree of nilpotency of commutator $C(C^3=0)$. In the present paper an explicit form of correlation function when the spectrum of $A_1$ and $A_2$ lies in zero is derived.