On generalizations of Boehmian space and Hartley transform

摘要

Boehmians are quotients of sequences which are constructed by using a set of axioms. In particular, one of these axioms states that the set S from which the denominator sequences are formed should be a commutative semigroup with respect to a binary operation. In this paper, we introduce a generalization of abstract Boehmian space, called generalized Boehmian space or G -Boehmian space, in which S is not necessarily a commutative semigroup. Next, we provide an example of a G -Boehmian space and we discuss an extension of the Hartley transform on it.