Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



On the Kotani-Last and Schrödinger conjectures

Author: Artur Avila
Journal: J. Amer. Math. Soc. 28 (2015), 579-616
MSC (2010): Primary 37H15; Secondary 47B39
Published electronically: June 11, 2014
MathSciNet review: 3300702
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the theory of ergodic one-dimensional Schrödinger operators, the ac spectrum has been traditionally expected to be very rigid. Two key conjectures in this direction state, on the one hand, that the ac spectrum demands almost periodicity of the potential, and, on the other hand, that the eigenfunctions are almost surely bounded in the essential support of the ac spectrum. We show how the repeated slow deformation of periodic potentials can be used to break rigidity, and disprove both conjectures.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 37H15, 47B39

Retrieve articles in all journals with MSC (2010): 37H15, 47B39

Additional Information

Artur Avila
Affiliation: CNRS, IMJ-PRG, UMR 7586, Univ Paris Diderot, Sorbonne Paris Cité, Sorbonnes Universités, UPMC Univ Paris 06, F-75013, Paris, France; IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brasil

Received by editor(s): October 11, 2012
Received by editor(s) in revised form: April 11, 2014
Published electronically: June 11, 2014
Article copyright: © Copyright 2014 American Mathematical Society