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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Perturbation of complete orthonormal sets and eigenfunction expansions.
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by Jerry L. Kazdan
Proc. Amer. Math. Soc. 27 (1971), 506-510
DOI: https://doi.org/10.1090/S0002-9939-1971-0271767-2

Abstract:

A technique is given for determining the asymptotic properties of vectors which are perturbations of a given basis—the eigenfunctions a selfadjoint operator. Its application is illustrated by a differential equation example, not using the Hilbert space norm. An estimate is also given for the codimension of the span of a perturbed set of vectors.
References
  • Garrett Birkhoff and Gian-Carlo Rota, Ordinary differential equations, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, 1962. MR 0138810
  • E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
  • T. Kato, Perturbation theory for linear operators, Die Grundlehren der math. Wissenschaften, Band 132, Springer-Verlag, New York, 1967. MR 34 #3324.
  • J. Schwartz, Perturbations of spectral operators, and applications. I. Bounded perturbations, Pacific J. Math. 4 (1954), 415–458. MR 63568, DOI 10.2140/pjm.1954.4.415
  • E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford, at the Clarendon Press, 1946 (German). MR 0019765
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Bibliographic Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 27 (1971), 506-510
  • MSC: Primary 47.48
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0271767-2
  • MathSciNet review: 0271767