Can you give an example of a function $f\in H^\infty(\Delta^2)$ with $f^{-1}\in L^\infty(T^2)$ but not inner? Here $H^\infty(\Delta^2)$ is the space of all bounded analytic functions defined on bi-disc $\Delta^2$ and $T^2$ is torus.
2026-03-25 07:40:07.1774424407
A function in $H^\infty(\Delta^2)$
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I'm not sure I understand your question. I assume that $f^{-1} = 1/f$? (The standard interpretation as the inverse of $f$ doesn't make sense.) Also, I assume that by inner you mean that the boundary value has modulus (suitably interpreted) has modulus $1$ almost everywhere.
If that is the case, almost any bounded zero-free holomorphic function will do. Take for example $f(z,w) = z-2$.