Waleed Noor: Invariant subspaces of polydisk Hardy spaces

Data: sexta-feira, 11 de dezembro de 2020, às 9h30.


Título: Invariant subspaces of polydisk Hardy spaces.

Resumo:  The shift-invariant subspaces of the classical Hardy space $H^2(\mathbb D)$ over the unit disk $\mathbb D$ were characterized in a landmark result by Arne Beurling in 1949. The analogous problem for polydisk Hardy spaces $H^2(\mathbb D^n)$ remains a major open problem in operator theory for $n > 1$. In this presentation we shall see how this problem is intimately related to the Invariant Subspace Problem (ISP) for finite $n > 1$ and to the Riemann Hypothesis (RH) when $n = \infty$.
The results in this presentation are based on joint works with Juan Carlos, Marcos Ferreira, João R. Carmo, and Charles Ferreira dos Santos.