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The spectrum of a one-dimensional pseudo-differential operator

Published online by Cambridge University Press:  24 October 2008

M. W. Wong
M. W. Wong
Affiliation:
Department of Mathematics, York University, Ontario, CanadaM3J 1P3
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Abstract

We describe the spectrum of a self-adjoint pseudo-differential operator on L2 (– ∞, ∞). We show that the essential spectrum coincides with the interval ([1, ∞) and give a lower bound for the lowest eigenvalue in (– ∞, 1). A sufficient condition for the existence of an eigenvalue in (– ∞, 1) is also given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 3 , November 1988 , pp. 575 - 580
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Beckner, W.. Inequalities in Fourier analysis. Ann. of Math. (2) 102 (1975), 159–182.CrossRefGoogle Scholar
[2]Eastham, M. S. P.Semi-bounded second-order differential operators. Proc. Roy. Soc. Edinburgh Sect. A 72 (1974), 9–16.Google Scholar
[3]Everitt, W. N.. On the spectrum of a second order linear differential equation with a p-integrable coefficient. Appl. Anal. 2 (1972), 143–160.CrossRefGoogle Scholar
[4]Schechter, M.. Spectra of Partial Differential Operators (North-Holland, 1971).Google Scholar
[5]Schechter, M.. Operator Methods in Quantum Mechanics (North-Holland, 1981).Google Scholar
[6]Schechter, M.. Spectra of Partial Differential Operators, Second Ed. (North-Holland, 1986).Google Scholar
[7]Veling, E. J. M.Optimal lower bounds for the spectrum of a second order linear differential equation with a p-integrable coefficient. Proc. Roy. Soc. Edinburgh Sect. A 92 (1982), 95–101.Google Scholar
[8]Wong, M. W.. On eigenvalues of pseudo-differential operators. Bull. London Math. Soc. 19 (1987), 63–66.CrossRefGoogle Scholar
[9]Wong, M. W.. A lower bound for the spectrum of a one-dimensional pseudo-differential operator. Math. Proc. Cambridge Philos. Soc. 103 (1988), 317–320.CrossRefGoogle Scholar