Author

Kouichi Taira

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Preprint Sep 2026

Large eigenvalues of the Connes-Moscovici operator

We prove the logarithmic Weyl law predicted by Connes and Moscovici for large positive eigenvalues of the distinguished self-adjoint extension of the operator $P=-\partial_x(x^2-1)\partial_x-4\pi^2x^2$ on the real line. More precisely, we use the WKB method and show a Bohr-Sommerfeld quantization rule characterizing su...

Kouichi Taira, Max Willems, M. Wrochna · 0 citations

Preprint Sep 2026

Modified wave operators are unbounded on $L^p$ for $p\neq 2$

We study the $L^p$-boundedness of Isozaki--Kitada type modified wave operators associated with Schr\"odinger operators $P=-\partial_x^2 + V$ in one dimension for potentials $V$ including long-range potentials such as negative Coulomb-like ones $V(x) = -(1+|x|^2)^{-\mu/2}$ for $\mu>0$. For such potentials, if $ \mu \in...

Akitoshi Hoshiya, Kouichi Taira · 0 citations