The defect index of singular symmetric linear difference equations with real coefficients
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- by Guojing Ren and Yuming Shi PDF
- Proc. Amer. Math. Soc. 138 (2010), 2463-2475 Request permission
Abstract:
This paper is concerned with the defect index of singular symmetric linear difference equations of order $2n$ with real coefficients and one singular endpoint. We show that their defect index $d$ satisfies the inequalities $n\leq d \leq 2n$ and that all values of $d$ 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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2607876