Integrable distributions and $\phi$-Fourier transform

Ganesan Chinnaraman

A new concept of integration of distributions is introduced and studied. It is proved that the space of all integrable distributions is properly larger than the space of Lebesgue integrable functions and compactly supported distributions. As an application of this concept, an alternate definition of Fourier transform namely $\phi$-Fourier transform is defined, on the space of integrable distributions into the space of continuous functions and its properties are established.