INTEGRABLE BOEHMIANS, FOURIER TRANSFORMS, AND POISSON’S SUMMATION FORMULA

The space of integrable Boehmians β`(R) contains a subspace which can be identified with L1(R). The Fourier transform can be defined for each element of β`(R). The Fourier transform of an integrable Boehmian is a continuous function which satisfies a growth condition. We investigate the Fourier transform on β`(R), and as an application, we extend Poisson’s summation formula to the space β`(R). 1