Zeros of entire functions represented by Fourier transforms

This talk will explore the properties of kernels that have Fourier transforms that are real entire functions with only real zeros. With the aid of the Mellin transform and the theory of multiplier sequences, several classical results of G. Pólya are extended. In addition, special attention is given to the finite Fourier transforms of the kernel $e^{-t^2}$. A related open problem posed by G. Csordas and C.-C. Yang is partially solved.

Link to thesis