Some Classes of Jacobi Matrices and Schrödinger Operators

dc.contributor.advisor	REMLING, CHRISTIAN
dc.contributor.author	HUR, INJO
dc.contributor.committeeMember	MILTON, KIM
dc.contributor.committeeMember	ALBERT, JOHN
dc.contributor.committeeMember	GRASSE, KEVIN
dc.contributor.committeeMember	RALF, SCHMIDT
dc.date.accessioned	2014-08-08T16:42:33Z
dc.date.available	2014-08-08T16:42:33Z
dc.date.issued	2014
dc.date.manuscript	2014-07
dc.description.abstract	This dissertation addresses two classes of Jacobi matrices and Schrödinger operators. First, we consider Jacobi matrices and Schrödinger operators that are reflectionless on an interval. We give a systematic development of a certain parametrization of this class, in terms of suitable spectral data, that is due to Marchenko. Then some applications of these ideas are discussed. In the second half, we study structural properties of the Lyapunov exponent $\gamma$ and the density of states $k$ for ergodic (or invariant) Jacobi matrices in a general framework. In this analysis, a central role is played by the function $w=-\gamma+i\pi k$ as a conformal map between certain domains. This idea goes back to Marchenko and Ostrovskii, who used this device in their analysis of the periodic problem.	en_US
dc.identifier.uri	http://hdl.handle.net/11244/10482
dc.language	en_US	en_US
dc.subject	Mathematics.	en_US
dc.thesis.degree	Ph.D.	en_US
dc.title	Some Classes of Jacobi Matrices and Schrödinger Operators	en_US
ou.group	College of Arts and Sciences::Department of Mathematics	en_US