IUMJ

Title: The spectrum of an Adelic Markov operator

Authors: Andreas Knauf

Issue: Volume 64 (2015), Issue 5, 1465-1512

Abstract:

For unitary representations of $\mathrm{SL}(2,\mathbb{Z})$, and with $\mathbf{L}$ and $\mathbf{R}$ representing $\left(\begin{smallmatrix}1&1\\0&1\end{smallmatrix}\right)$ (respectively, $\left(\begin{smallmatrix}1&0\\1&1\end{smallmatrix}\right)$), we analyze the operators $\mathbf{T}:=\frac{1}{2}(\mathbf{L}+\mathbf{R})$.