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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Criteria for discrete spectrum of singular selfadjoint differential operators
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by L. W. Rollins PDF
Proc. Amer. Math. Soc. 34 (1972), 195-200 Request permission


Under certain conditions on the coefficients of symmetric singular differential operators of order 2n, selfadjoint extensions are shown to have a discrete spectrum. The results are proven specifically for the Friedrichs extension.
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  • M. S. P. Eastham, The least limit point of the spectrum associated with singular differential operators, Proc. Cambridge Philos. Soc. 67 (1970), 277–281. MR 252740, DOI 10.1017/s0305004100045552
  • K. O. Friedrichs, Criteria for the discrete character of the spectra of ordinary differential operators, Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948, Interscience Publishers, Inc., New York, 1948, pp. 145–160. MR 0023415
  • M. A. Naĭmark, Linear differential operators, GITTL, Moscow, 1954; English transl., Part II, Ungar, New York, 1967. MR 16, 702; MR 41 #7485.
  • Frédéric Riesz and Béla Sz.-Nagy, Leçons d’analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1953 (French). 2ème éd. MR 0056821
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 195-200
  • MSC: Primary 47E05; Secondary 34B25
  • DOI:
  • MathSciNet review: 0291883