The defect index of singular symmetric linear difference equations with real coefficients

Authors:
Guojing Ren and Yuming Shi

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2463-2475

MSC (2010):
Primary 39A70, 34B20

DOI:
https://doi.org/10.1090/S0002-9939-10-10253-6

Published electronically:
February 24, 2010

MathSciNet review:
2607876

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the defect index of singular symmetric linear difference equations of order with real coefficients and one singular endpoint. We show that their defect index satisfies the inequalities and that all values of in this range are realized. This parallels the well known result of Glazman for differential equations established about 1950. In addition, several criteria of the limit point and strong limit point cases are established.

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Additional Information

**Guojing Ren**

Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China – and – School of Statistics and Mathematics, Shandong Economic University, Jinan, Shandong 250014, People’s Republic of China

Email:
rgjmaths@gmail.com

**Yuming Shi**

Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China

Email:
ymshi@sdu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-10-10253-6

Keywords:
Singular symmetric linear difference equation,
square summable solution,
defect index,
limit point case,
strong limit point case.

Received by editor(s):
July 6, 2009

Received by editor(s) in revised form:
October 9, 2009

Published electronically:
February 24, 2010

Additional Notes:
This research was supported by the NNSF of Shandong Province (Grant Y2006A15).

Communicated by:
Nigel J. Kalton

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.