Unbounded Jacobi matrices at critical coupling

Authors:
David Damanik;Serguei Naboko
Affiliations:
Department of Mathematics, Rice University, Houston, TX 77005, USA;Department of Mathematical Physics, Institute of Physics, St. Petersburg University, Ulianovskaia 1, 198904 St. Petergoff, St. Petersburg, Russia
Venue:
Journal of Approximation Theory
Year:
2007

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Abstract

We consider a class of Jacobi matrices with unbounded coefficients. This class is known to exhibit a first-order phase transition in the sense that, as a parameter is varied, one has purely discrete spectrum below the transition point and purely absolutely continuous spectrum above the transition point. We determine the spectral type and solution asymptotics at the transition point.