Geodesic
Lower Bounds for the Essential Spectrum of Fourth-Order Differential Operators
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 460-465

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we seek to determine the greatest lower bound of the essential spectrum of self-adjoint singular differential operators of the form 1 where 0 ≦ x < ∞. In the event that this bound is + ∞, our results will yield criteria for the discreteness of the spectrum of (1).Such bounds have been established by Friedrichs (3) for Sturm-Liouville operators of the form and our techniques will be closely related to those of (3). However, instead of studying the solutions of 2 directly, we shall exploit the intimate connection between the infimum of the essential spectrum of (1) and the oscillation properties of (2). 
Kreith, Kurt. Lower Bounds for the Essential Spectrum of Fourth-Order Differential Operators. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 460-465. doi: 10.4153/CJM-1969-050-6
@article{10_4153_CJM_1969_050_6,
     author = {Kreith, Kurt},
     title = {Lower {Bounds} for the {Essential} {Spectrum} of {Fourth-Order} {Differential} {Operators}},
     journal = {Canadian journal of mathematics},
     pages = {460--465},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-050-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-050-6/}
}
TY  - JOUR
AU  - Kreith, Kurt
TI  - Lower Bounds for the Essential Spectrum of Fourth-Order Differential Operators
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 460
EP  - 465
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-050-6/
DO  - 10.4153/CJM-1969-050-6
ID  - 10_4153_CJM_1969_050_6
ER  - 
%0 Journal Article
%A Kreith, Kurt
%T Lower Bounds for the Essential Spectrum of Fourth-Order Differential Operators
%J Canadian journal of mathematics
%D 1969
%P 460-465
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-050-6/
%R 10.4153/CJM-1969-050-6
%F 10_4153_CJM_1969_050_6

[1] 1. Akhiezer, N. I. and Glazman, I. M., Theory of linear operators in Hilbert space, Vol. II (Ungar, New York, 1963). Google Scholar

[2] 2. Dunford, N. and Schwartz, J., Linear operators, Part II (Interscience, New York, 1963). Google Scholar

[3] 3. Friedrichs, K. O., Criteria for discrete spectra, Comm. Pure Appl. Math. 3 (1950), 439–449. Google Scholar

[4] 4. Hinton, D., Clamped end boundary conditions for fourth-order self-adjoint differential equations, Duke Math. J. 44 (1967), 131–138. Google Scholar

[5] 5. Howard, H., Oscillation criteria for fourth-order linear differential equations, Trans. Amer. Math. Soc. 96 (1960), 296–311. Google Scholar

[6] 6. Kreith, K., An abstract oscillation theorem, Proc. Amer. Math. Soc. 19 (1968), 17–20. Google Scholar

[7] 7. Leighton, W. and Nehari, Z., On the oscillation of solutions of self-adjoint linear differential equations of fourth order, Trans. Amer. Math. Soc. 89 (1958), 325–377. Google Scholar

[8] 8. Riesz, F. and -Nagy, B. Sz., Functional analysis (Ungar, New York, 1955). Google Scholar

Cité par Sources :