Search

The theory of Fourier transform on spaces of Boehmians is well known. Several spaces of Boehmians are constructed, and the Fourier transform on these spaces are defined and investigated in the recent literature. Most recently, Dennis Nemzer introduced a new space of Boehmians [image omitted] called the space of integrable Boehmians, which is properly larger than the space [image omitted] of all integrable functions on [image omitted] (the real axis) and investigates the theory of Fourier transform on this space. In this article, we shall find a necessary and sufficient condition for a continuous function to be the Fourier transform of some integrable Boehmian. This answers a question raised by Nemzer. [ABSTRACT FROM AUTHOR]