Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. V. Atkinson, Limit-n criteria of integral type, Proc.Royal Soc. Edinb.(A), 73(1975), 167–198.
I. Brinck, Self-adjointness and spectra of Sturm-Liouville operators, Math. Scand. 7(1959), 219–239.
N. Dunford and J. T. Schwartz, Linear Operators. Part II, (Interscience, New York, 1963).
M. S. P. Eastham, Gaps in the essential spectrum associated with singular differential operators, Quart. Jour. Math. (Oxford) (2), 18(1967), 155–168.
M. S. P. Eastham, Asymptotic estimates for the lengths of the gaps in the essential spectrum of self-adjoint differential operators, Proc. Yoral Soc. Edinb.(A), 74(1976), 239–252.
M. S. P. Eastham, Gaps in the essential spectrum of even-order self-adjoint differential operators, Proc. London Math. Soc.(3), 34(1977), 213–230.
W. N. Everitt, On the spectrum of a second-order linear differential equation with a p-integrable coefficient, Applicable Analysis, 2(1972), 143–160.
I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, (Israel Program for Scientific Translations, Jerusalem, 1965).
S. G. Halvorsen, Counterexamples in the spectral theory of singular Sturm-Liouville operators, Mathematics no. 9/74, Matematisk Institutt, Universitet i Trondheim, Trondheim, Norway.
P. Hartman and C. R. Putnam, The gaps in the essential spectra of gave equations, Amer. Jour. Math. 72(1950), 849–862.
R. M. Kauffman, On the growth of solutions in the oscillatory case, Proc. Amer. Math. Soc. 51(1975), 49–54
R. M. Kauffman, Gaps in the essential spectrum for second order systems, Proc. Amer. Math. Soc. 51(1975), 55–61.
A. C. Lazer, A stability condition for the differential equation y″+p(x)y=0, Michigan Math. Jour. 12(1965), 193–196.
C. R. Putnam, On isolated eigenfunctions associated with bounded potentials, Amer. Jour. Math. 82(1950), 135–147.
D. A. R. Rigler, On a strong limit-point condition and an integral inequality associated with a symmetric matrix differential expression, Proc. Royal Soc. Edinb. (A), 76(1976), 155–159.
L. B. Zelenko, Spectrum of Schrödinger's equation with a complex pseudoperiodic potential, Parts I and II, Diff. Urav. 12(1976), 806–814 and 1417–1426.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this paper
Cite this paper
Atkinson, F.V. (1980). Exponential behaviour of eigenfunctions and gaps in the essential spectrum. In: Everitt, W.N. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091372
Download citation
DOI: https://doi.org/10.1007/BFb0091372
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10252-6
Online ISBN: 978-3-540-38346-8
eBook Packages: Springer Book Archive