Discrete spectra criteria for singular difference operators

Simón Peňa

Mathematica Bohemica (1999)

  • Volume: 124, Issue: 1, page 35-44
  • ISSN: 0862-7959

Abstract

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We investigate oscillation and spectral properties (sufficient conditions for discreteness and boundedness below of the spectrum) of difference operators B(y)n+k = (-1)nwk n (pk n yk).

How to cite

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Peňa, Simón. "Discrete spectra criteria for singular difference operators." Mathematica Bohemica 124.1 (1999): 35-44. <http://eudml.org/doc/248466>.

@article{Peňa1999,
abstract = {We investigate oscillation and spectral properties (sufficient conditions for discreteness and boundedness below of the spectrum) of difference operators B(y)n+k = (-1)nwk n (pk n yk).},
author = {Peňa, Simón},
journal = {Mathematica Bohemica},
keywords = {discrete spectrum; property BD; discrete variational principle; discrete Wirtinger’s inequality; singular difference operators; oscillation; difference operator; discrete spectrum; property BD; discrete variational principle; discrete Wirtinger's inequality; singular difference operators; oscillation},
language = {eng},
number = {1},
pages = {35-44},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Discrete spectra criteria for singular difference operators},
url = {http://eudml.org/doc/248466},
volume = {124},
year = {1999},
}

TY - JOUR
AU - Peňa, Simón
TI - Discrete spectra criteria for singular difference operators
JO - Mathematica Bohemica
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 124
IS - 1
SP - 35
EP - 44
AB - We investigate oscillation and spectral properties (sufficient conditions for discreteness and boundedness below of the spectrum) of difference operators B(y)n+k = (-1)nwk n (pk n yk).
LA - eng
KW - discrete spectrum; property BD; discrete variational principle; discrete Wirtinger’s inequality; singular difference operators; oscillation; difference operator; discrete spectrum; property BD; discrete variational principle; discrete Wirtinger's inequality; singular difference operators; oscillation
UR - http://eudml.org/doc/248466
ER -

References

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  2. Bohner M., Došlý O., 10.1216/rmjm/1181071889, Rocky Mountain J. Math. 27 (1997), 707-743. (1997) MR1490271DOI10.1216/rmjm/1181071889
  3. Došlý O., Reciprocity principle for Sturm-Liouville difference equations and some of its applications, Proceedings of SICDEA. Veszprem, 1995, pp. 145-153. (1995) MR1636320
  4. Hinton D. B., Lewis R. T., 10.1016/0022-247X(78)90088-4, J. Math. Anal. Appl. 63 (1978), 421-438. (1978) Zbl0392.39001MR0611455DOI10.1016/0022-247X(78)90088-4
  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. (1975) Zbl0298.34018MR0367358
  6. Hartman P., Difference equations: disconjugacy, principal solutions, Green's function, complete monoticity, Trans. Amer. Math. Soc. 246 (1978), 1-30. (1978) MR0515528

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