Idele characters in spectral synthesis on
Let , . We construct Dirichlet series where for each fixed in a half plane, , as a function of , is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when .