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

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