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Published July 2006 | Submitted
Journal Article Open

Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szegő asymptotics

Abstract

We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence of Szegő asymptotics and of Jost asymptotics for the Weyl solution. We also prove L^2 convergence of Szegő asymptotics on the spectrum.

Additional Information

© 2006 Springer-Verlag. Received: 22 February 2005; Accepted: 10 October 2005; First Online: 09 January 2006. Supported in part by NSF grant DMS-0227089. Supported in part by NSF grant DMS-0140592 and in part by Grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

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August 19, 2023
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