Spectral properties of general self-adjoint, even order differential operators

Roman Hilscher

Mathematica Slovaca (2000)

  • Volume: 50, Issue: 2, page 165-186
  • ISSN: 0139-9918

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Hilscher, Roman. "Spectral properties of general self-adjoint, even order differential operators." Mathematica Slovaca 50.2 (2000): 165-186. <http://eudml.org/doc/34512>.

@article{Hilscher2000,
author = {Hilscher, Roman},
journal = {Mathematica Slovaca},
keywords = {non(oscillatory) equation; reciprocity principle; linear Hamiltonian systems; spectrum},
language = {eng},
number = {2},
pages = {165-186},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Spectral properties of general self-adjoint, even order differential operators},
url = {http://eudml.org/doc/34512},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Hilscher, Roman
TI - Spectral properties of general self-adjoint, even order differential operators
JO - Mathematica Slovaca
PY - 2000
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 50
IS - 2
SP - 165
EP - 186
LA - eng
KW - non(oscillatory) equation; reciprocity principle; linear Hamiltonian systems; spectrum
UR - http://eudml.org/doc/34512
ER -

References

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  1. AHLBRANDT C. D., Equivalent boundary value problems for self-adjoint differential systems, J. Differential Equations 9 (1971), 420-435. (1971) Zbl0218.34020MR0284636
  2. AHLBRANDT C. D.-HINTON D. B.-LEWIS R. T., The effect of variable change on oscillation and disconjugacy criteria with applications to spectral theory and asymptotic theory, J. Math. Anal. Appl. 81 (1981), 234-277. (1981) Zbl0459.34018MR0618771
  3. COPPEL W. A., Disconjugacy, Lectures Notes in Math. 220, Springer-Verlag, Berlin-Heidelberg, 1971. (1971) Zbl0224.34003MR0460785
  4. DOŠLÝ O., Transformations of linear Hamiltonian systems preserving oscillatory behaviour, Arch. Math. (Brno) 27b (1991), 211-219. (1991) Zbl0764.34026MR1189218
  5. DOŠLÝ O., Generalized reciprocity for self-adjoint linear differential equations, Arch. Math. (Brno) 31 (1995), 85-96. (1995) Zbl0841.34032MR1357977
  6. DOŠLÝ O., Oscillation and spectral properties of a class of singular self-adjoint differential operators, Math. Nachr. 188 (1997), 49-68. (1997) Zbl0889.34029MR1484668
  7. DOŠLÝ O.-HILSCHER R., Spectral properties of fourth order differential operators, Math. Bohemica 122 (1997), 153-168. (1997) Zbl0894.34028MR1460945
  8. GLAZMAN I. M., Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators, Israel Program for Scientific Тranslations; Daniel Davey & Co., Inc, Jerusalem; New York, 1965; 1966. (1965) Zbl0143.36505MR0190800
  9. HARТMAN P., Self-adjoint, non-oscillatory systems of ordinary, second order, linear differential equations, Duke J. Math. 24 (1956), 25-35. (1956) MR0082591
  10. HINТON D. B.-LEWIS R. Т., Discrete spectra criteria for singular differential operators with middle terms, Math. Proc Cambridge Philos. Soc 77 (1975), 337-347. (1975) MR0367358
  11. NAIMARK M. A., Linear Differential Operators, Part II, Ungar, New York, 1968. (1968) Zbl0227.34020MR0353061
  12. REID W. Т., Sturmian Theory for Ordinary Differential Equations, Springeг-Verlag, New York-Berlin-Heidelberg, 1980. (1980) Zbl0459.34001MR0606199
  13. STERNBERG R. L., Variational methods and nonoscillatory theorems for systems of differential equations, Duke J. Math. 19 (1952), 311-322. (1952) MR0048668
  14. WEIDMANN J., Linear Operators in Hilbert Spaces, New York-Berlin-Heidelberg, 1980. (1980) Zbl0434.47001MR0566954

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