Operational calculus on fourier-stieltjes transform

Fourier and Stieltjes transforms represent an important area of analysis and properties of it are more elegant. The Fourier transform is most significant in functional analysis, complex analysis, number theory, representation theory etc. Also, Fourier transform has applicable in many areas such as image processing, time series analysis, antenna design, radar system, human auditory system etc. In the same way, the Stieltjes transform is also a basic tool for analyzing the behavior of many important functions in mathematics and mathematical physics. As it is well known, the Stieltjes transform can be regarded as an eigenvalue moment generating function. The Stieltjes transform have many applications in many areas such as statistics, probability, moment problems, it is a key tool to derive information and communication theoretic performance measures for random vector channels; it can be used to express more intuitive performance measures of communication systems such as signal to interference, noise ratios and channel capacity etc. In this paper we present Operational calculus on Fourier-Stieltjes Transform.