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

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.

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

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

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

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

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

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

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