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Proceedings of the American Mathematical Society

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Perturbation of complete orthonormal sets and eigenfunction expansions.

Author: Jerry L. Kazdan
Journal: Proc. Amer. Math. Soc. 27 (1971), 506-510
MSC: Primary 47.48
MathSciNet review: 0271767
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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 [Enhancements On Off] (What's this?)

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  • [2] E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
  • [3] T. Kato, Perturbation theory for linear operators, Die Grundlehren der math. Wissenschaften, Band 132, Springer-Verlag, New York, 1967. MR 34 #3324.
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Keywords: Eigenfunctions, perturbation, Schauder basis, asymptotic
Article copyright: © Copyright 1971 American Mathematical Society

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