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
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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
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