Counterexamples to the Kotani-Last conjecture for continuum Schrodinger operators via character-automorphic Hardy spaces

摘要

The Kotani Last conjecture states that every ergodic operator in one space dimension with non-empty absolutely continuous spectrum must have almost periodic coefficients. This statement makes sense in a variety of settings; for example, discrete Schrodinger operators, Jacobi matrices, CMV matrices, and continuum Schrodinger operators.