On zero sets in Fock spaces

Maximal Zero Sequences for Fock Spaces

A sequence Z in the complex plane C is called a zero sequence for the Fock space F p α if there exists a function f ∈ F p α , not identically zero, such that Z is the zero set of f , counting multiplicities. We show that there exist zero sequences Z for F p α with the following properties: (1) For any a ∈ C the sequence Z ∪ {a} is no longer a zero sequence for F p α; (2) the space IZ consisting...

Zero Sets for Spaces of Analytic Functions

We show that under mild conditions, a Gaussian analytic function F that a.s. does not belong to a given weighted Bergman space or Bargmann–Fock space has the property that a.s. no non-zero function in that space vanishes where F does. This establishes a conjecture of Shapiro (1979) on Bergman spaces and allows us to resolve a question of Zhu (1993) on Bargmann–Fock spaces. We also give a simila...

Curiosities on Free Fock Spaces

We consider some curious aspects of single-species free Fock spaces, such as novel bosonization and fermionization formulae and relations to various physical properties of bosonic particles. We comment on generalizations of these properties to physically more interesting many-species free Fock spaces.

Toeplitz Operators on Fock Spaces

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 preserving stability (due to Borcea and the author) to the realm of entire functions, and translates into an optimal, albeit formal, Lee–Yang theorem.