Spectral measure of the transition operator and harmonic functions connected with random walks on discrete groups

On the spectrum of a random walk on the

On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper's operator

✍ Cédric Béguin; Alain Valette; Andrzej Zuk 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 908 KB

Harper's operator is the self-adjoint operator on 12(7/) defined by Ho,o~(n) = ~(n + 1) + se(n -1 ) + 2 cos(2zr(n0 + (p))~(n) (~ ~ l 2 (7/), n 6 7/, 0, (p c [0, I ]). We first show that the determination of the spectrum of the transition operator on the Cayley graph of the discrete Heisenberg group