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Proceedings of the American Mathematical Society

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On semibounded differential operators


Author: Harry Hochstadt
Journal: Proc. Amer. Math. Soc. 35 (1972), 298-300
MSC: Primary 47E05; Secondary 34B25
DOI: https://doi.org/10.1090/S0002-9939-1972-0308858-4
MathSciNet review: 0308858
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Abstract: It is shown that regular ordinary differential operators have a semibounded spectrum. The proof requires fewer prerequisites than other proofs found in the literature and also yields estimates on the lower bound of the spectrum.


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  • [1] Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, With the assistance of William G. Bade and Robert G. Bartle, Interscience Publishers John Wiley & Sons New York-London, 1963. MR 0188745
  • [2] M. A. Naĭmark, Linear differential operators. Vol. II, GITTL, Moscow, 1954; English transl., Ungar, New York, 1967, pp. 93 ff. MR 16, 702; MR 41 #7485.
  • [3] Harold Widom, Lectures on integral equations, Notes by David Drazin and Anthony J. Tromba. Van Nostrand Mathematical Studies, No. 17, Van Nostrand; Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0243299

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DOI: https://doi.org/10.1090/S0002-9939-1972-0308858-4
Article copyright: © Copyright 1972 American Mathematical Society