What is "boehmians"

In mathematics, Boehmians are objects obtained by an abstract algebraic construction of "quotients of sequences." The original construction was motivated by regular operators introduced by T. K. Boehme. Regular operators are a subclass of Mikusiński operators, that are defined as equivalence classes of convolution quotients of functions on [0, ∞). The original construction of Boehmians gives us a space of generalized functions that includes all regular operators and has the algebraic character of convolution quotients. On the other hand, it includes all distributions eliminating the restriction of regular operators to [0, ∞).

Since the Boehmians were introduced in 1981, the framework of Boehmians has been used to define a variety of spaces of generalized functions on R and generalized integral transforms on those spaces. It was also applied to function spaces on other domains, like locally compact groups and manifolds.