| Title:
|
Discrete spectra criteria for singular difference operators (English) |
| Author:
|
Peňa, Simón |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
35-44 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate oscillation and spectral properties (sufficient conditions for discreteness and boundedness below of the spectrum) of difference operators
B(y)_{n+k} = {{(-1)}^n\over w_k} \Delta^n (p_k \Delta^n y_k). (English) |
| Keyword:
|
discrete spectrum |
| Keyword:
|
property BD |
| Keyword:
|
discrete variational principle |
| Keyword:
|
discrete Wirtinger’s inequality |
| Keyword:
|
singular difference operators |
| Keyword:
|
oscillation |
| Keyword:
|
difference operator |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| MSC:
|
39A70 |
| MSC:
|
47A10 |
| MSC:
|
47B39 |
| idZBL:
|
Zbl 0936.39008 |
| idMR:
|
MR1687425 |
| DOI:
|
10.21136/MB.1999.125980 |
| . |
| Date available:
|
2009-09-24T21:34:50Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125980 |
| . |
| Reference:
|
[1] Bohner M.: Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions.J. Math. Anal. Appl. 199 (1996), 804-826. MR 1386607, 10.1006/jmaa.1996.0177 |
| Reference:
|
[2] Bohner M., Došlý O.: Disconjugacy and transformations for symplectic systems.Rocky Mountain J. Math. 27 (1997), 707-743. MR 1490271, 10.1216/rmjm/1181071889 |
| Reference:
|
[3] Došlý O.: Reciprocity principle for Sturm-Liouville difference equations and some of its applications.Proceedings of SICDEA. Veszprem, 1995, pp. 145-153. MR 1636320 |
| Reference:
|
[4] Hinton D. B., Lewis R. T.: Spectral analysis of second order difference equations.J. Math. Anal. Appl. 63 (1978), 421-438. Zbl 0392.39001, MR 0611455, 10.1016/0022-247X(78)90088-4 |
| Reference:
|
[5] Hinton D. B., Lewis R. T.: Discrete spectra criteria for singular differential operators with middle terms.Math. Proc. Cambridge Philos. Soc. 77 (1975), 337-347. Zbl 0298.34018, MR 0367358 |
| Reference:
|
[6] Hartman P.: Difference equations: disconjugacy, principal solutions, Green's function, complete monoticity.Trans. Amer. Math. Soc. 246 (1978), 1-30. MR 0515528 |
| . |
