Jacobi matrices with absolutely

continuous spectrum

Authors:
Jan Janas and Serguei Naboko

Journal:
Proc. Amer. Math. Soc. **127** (1999), 791-800

MSC (1991):
Primary 47B37; Secondary 47B39

DOI:
https://doi.org/10.1090/S0002-9939-99-04586-4

MathSciNet review:
1469415

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Jacobi matrix defined in as , where is a unilateral weighted shift with nonzero weights such that Define the seqences: If and , then has an absolutely continuous spectrum covering . Moreover, the asymptotics of the solution is also given.

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Additional Information

**Jan Janas**

Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Cracow Branch, Sw. Tomasza 30, 31-027 Krakow, Poland

Email:
najanas@cyf-kr.edu.pl

**Serguei Naboko**

Affiliation:
Department of Mathematical Physics, Institute for Physics, St. Petersburg University, Ulianovskaia 1, 198904, St. Petergoff, Russia

Email:
naboko@snoopy.phys.spbu.ru

DOI:
https://doi.org/10.1090/S0002-9939-99-04586-4

Keywords:
Jacobi matrix,
absolutely continuous spectrum,
asymptotics behaviour

Received by editor(s):
June 25, 1997

Additional Notes:
The research of the first author was supported by grant PB 2 PO3A 002 13 of the Komitet Badań Naukowych, Warsaw.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1999
American Mathematical Society