21st Century COE Program : Mathematics of Nonlinear Structure via Singularity

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.

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