Rajkamal Naiwal: Beurling's Theorem and Invariant Subspaces

Abstract: The classical Beurling theorem is a powerful and celebrated result in operator theory, closely tied to the invariant subspace problem—one of the central questions in the field. It gives a complete description of the invariant subspaces of the unilateral shift on the Hardy space $H^2$, showing that each nontrivial closed shift-invariant subspace is of the form $\phi H^2$, where $\phi$ is an inner function.

In this talk, we introduce the Hardy space, define invariant subspaces and inner functions, and discuss a proof of Beurling’s theorem.

The seminar now has a homepage with the planned talks for the entire semester: https://mathematical-conversations.splet.arnes.si/