## Kouhei Izuchi : The 12th COE Lecture Series

### I) Cyclic vectors in the Segal-Bargmann space

We study invariant subspaces and cyclic vectors in the Segal-Bargmann space. First we introduce some results about them in Hardy space and Bergman space. Next, we characterize cyclic vectors in the Segal-Bargmann space and we compare them with ones in Hardy space and Bergman space.

### II) Cross commutators on backward shift invariant subspaces over the bidisk

In this talk, we introduce Manderkar's theorem and we study a classification by cross commutators on invariant subspaces and backward shift invariant subspaces in Hardy space over the bidisk.