Paley-Wiener type theorems by transmutations

The classical Paley-Wiener theorem for functions in L _dx ² relates the growth of the Fourier transform over the complex plane to the support of the function. In this work we obtain Paley-Wiener type theorems where the Fourier transform is replaced by transforms associated with self-adjoint operators on L _dμ ² , with simple spectrum, where dμ is a Lebesgue-Stieltjes measure. This is achieved via the use of support preserving transmutations. Communicated by Paul L. Butzer