On a spectral property of Jacobi matrices

Author:
S. Kupin

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1377-1383

MSC (2000):
Primary 47B36; Secondary 42C05

Published electronically:
December 12, 2003

MathSciNet review:
2053342

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Jacobi matrix with elements on the main diagonal and elements on the auxiliary ones. We suppose that is a compact perturbation of the free Jacobi matrix. In this case the essential spectrum of coincides with , and its discrete spectrum is a union of two sequences , tending to . We denote sequences and by and , respectively.

The main result of the note is the following theorem.

**Theorem.**Let be a Jacobi matrix described above and be its spectral measure. Then if and only if

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Additional Information

**S. Kupin**

Affiliation:
Department of Mathematics, Box 1917, Brown University, Providence, Rhode Island 02912

Email:
kupin@math.brown.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-07244-7

Keywords:
Jacobi matrices,
sum rules

Received by editor(s):
October 25, 2002

Published electronically:
December 12, 2003

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2003
American Mathematical Society