Exact and Numerical Inversion of Pseudo-differential Operators and Applications to Signal Processing
A large class of time-varying filters can be described via pseudo-differential operators belonging to the Hormander class OPS 0 0 , 0. The questions whether and how an input signal can be reconstructed from a known output lead to the problems of invertibility of pseudo-differential operators in that class and of (at least, numerical) solution of pseudo-differential equations. We are going to derive effective conditions for the invertibility for pseudo-differential operators with globally slowly varying symbols as well as for causal pseudo-differential operators, and we study the stability of the finite sections method with respect to time and frequency for these operators.
Abstract In this paper, we obtain the distribution of mixed sum of two independent random variables with different probability density functions. One with probability density function defined in finite range and the other with probability density function defined in infinite range and associated with product of Srivastava's polynomials and H-function. We use the Laplace transform and its inverse to obtain our main result. The result obtained here is quite general in nature and is capable of yielding a large number of corresponding new and known results merely by specializing the parameters involved therein. To illustrate, some special cases of our main result are also given.