On generalizations of Boehmian space and Hartley transform

Abstract

Boehmians are quotients of sequences which areconstructed by using a set of axioms. In particular, one of theseaxioms states that the set $S$ from which the denominatorsequences are formed should be a commutative semigroup withrespect to a binary operation. In this paper, we introduce ageneralization of abstract Boehmian space, called generalizedBoehmian space or $G$-Boehmian space, in which $S$ is notnecessarily a commutative semigroup. Next, we provide an exampleof a $G$-Boehmian space and we discuss an extension of the Hartleytransform on it.