Convolution Product And Fourier-Cosine Transform Of Functions, Measures And Distributions

We consider in this chapter spaces of even functions on E . We define on these spaces the translation operators o^, x > 0, the convolution product *Q and the Fourier-

cosine transform 3^ , respectively by

We define also the convolution product *Q and the Fourier-cosine transform on

the space of complex bounded measures on [0, + <*>[ and on even distributions on E.