Preprint
Sep 2026
Invariant sets of the double Hilbert transform
We present an example that shows that the double Hilbert transform $\H$ can have the characteristic function of an open set of finite measure in $\mathbb{R} \times \mathbb{R}$ as an approximate eigenvector for the eigenvalue $1$. The same holds for the dyadic model of $\H$, the double dyadic shift. We further construct...
E. Abakumov, K. Domelevo, S. Petermichl et al.
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