On numerical invariants for homogeneous submodules in H² (D²)

The Hardy space H² (D²) can be viewed as a module over the polynomial ring C [z, w] with module action defined by multiplica-tion of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H² (D²), and it gives rise to some in-teresting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes these invariants for homogeneous submodules through Toeplitz determinants.