M. Wrochna

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...