functional analysis

On numerical invariants for submodules $[(z - w)^{2}]$ in $H^{2} (D^{2})$

arXiv:2604.22289 · doi:10.1007/s40840-026-02132-3

summary

The paper derives explicit formulas for numerical invariants of the homogeneous submodule generated by (z‑w)^2 in the Hardy module over the bidisk and checks a monotonicity property for this case.

Abstract

In this paper, we study numerical invariants associated with a homogeneous submodule of the Hardy module over the bidisk. We focus on the submodule generated by the polynomial $(z - w)^{2}$ and obtain explicit formulas for the corresponding invariants. As an application, we verify the monotonicity property in this concrete setting. Our results provide a detailed example illustrating the behavior of these invariants beyond the linear case.

Topics & keywords

#hardy spaces #bidisk #submodule invariants #operator theory #several complex variablesHardy modulebidisk(z-w)^2numerical invariantsmonotonicity propertyhomogeneous submodule

On numerical invariants for submodules [(z−w)2] in H2(D2)

Abstract

Topics & keywords

On numerical invariants for submodules $[(z - w)^{2}]$ in $H^{2} (D^{2})$