A Spectral Representation of a Class of Nonstationary Processes

Abstract

In this paper, an extension of the weakly harmonizable class of processes is considered. This class, termed almost periodic contractive harmonizable, is based upon the natural contractive operator associated with harmonizable processes. A spectral representation of these processes is obtained. A relation between the almost periodic contractive harmonizable and the oscillatory harmonizable classes is considered. The paper concludes with a series representation for the almost periodic contractive harmonizable class.

Key Words:

• Harmonizable processes
• Oscillatory processes
• Semi-groups of contractive operators
• Almost periodic functions