Sesión Análisis armónico, real y teoría de aproximaciónSampling properties of the zeroes of the Gaussian entire function
Joaquín Camilo Singer
Universidad de Buenos Aires, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
We study sampling properties of the zero set of the Gaussian entire function on Fock spaces. Firstly, we relax Seip and Wallstén's density and separation conditions for sampling sets on Fock spaces to obtain weighted inequalities for sets that are not necessarily sampling. On the probabilistic front, we estimate the number of zeroes of the Gaussian entire functions that are close to each other. We use these to prove random sampling inequalities for polynomials of degree at most $d$ using ${d}+o(d)$ points, and show that, with high probability, the sampling constants grow slower than $d^\varepsilon$ for any $\varepsilon \gt 0$ . In particular, we recover a result from Lyons and Zhai in the case of the Gaussian entire function, where it is shown that the zeroes are (almost surely) a uniqueness set for the Fock space.
Trabajo en conjunto con: Jeremiah Buckley (King's College London, United Kingdom) y Felipe Marceca (Acoustics Research Institute - Austrian Academy of Sciences, Austria).