IJPAM: Volume 95, No. 2 (2014)

ON THE FORM OF CORRELATION FUNCTION FOR
A CLASS OF NONSTATIONARY FIELD WITH
A DISCRETE AND MIXED SPECTRUM

Rae'd Hatamleh
Department of Mathematics
Faculty of Science and Technology
Jadara University
21110 Irbid, JORDAN


Abstract. The present paper is devoted to the derivation of an explicit form of linearly representable random fields in the form $h(x_1,x_2)=\exp {\{i(x_1A_1+x_2A_2)\}}$ $h,$ 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 in [3], [5], [7].

It is shown that a rank of nonstationary of field $h(x_{1},x_{2})$ depends not only on a degree of non-self adjoint 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 for discrete spectrum of $A_{1}$ and $A_{2}$ is derived. A form in the case of spectrum of operator $A_1$ is constructed in zero and that of the operator $A_2$ is pure discrete of $A_{1}$and $A_{2}$ is zero and the other is discrete, is obtained.

Received: March 21, 2014

AMS Subject Classification: 47D38, 60GXX, 60G20

Key Words and Phrases: correlation function, triangular model, nonstationary field, zero spectrum, discrete and mixed spectrum

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DOI: 10.12732/ijpam.v95i2.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 95
Issue: 2
Pages: 149 -


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