THE LEE-YANG AND PÓLYA-SCHUR PROGRAMS. III. ZERO-PRESERVERS ON BARGMANN-FOCK SPACES.

We characterize linear operators preserving zero-restrictions on entire functions in weighted Bargmann-Fock spaces. This extends the characterization of linear operators on polynomials preserv- ing stability (due to Borcea and the author) to the realm of entire functions, and translates into an optimal, albeit formal, Lee-Yang theorem. [ABSTRACT FROM AUTHOR]