The theory of Schwartz Distributions opened up a new area of mathematical research, which in turn has provided an impetus in the development of a number of mathematical disciplines, such as ordinary and partial differential equations, operational calculus, transformation theory and functional analysis. The integral transforms and generalized functions have also shown equivalent association of Boehmians and the integral transforms. The theory of Boehmians, which is a generalization of Schwartz distributions are discussed in this paper. Further, exchange property is defined to construct Mehler-Fock transform of tempered Boehmians. We investigate exchange property for the Mehler-Fock transform by using the theory of Mehler-Fock transform of distributions. Algebraic properties and convergence is also proved for this relation on the tempered Boehmians which is a natural extension of tempered distribution.
On the Exchange Property for the Mehler-Fock Transform,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 11,
2, Article 22.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss2/22