Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The $ L\sp{p}$ behavior of eigenfunction expansions

Author: Harold E. Benzinger
Journal: Trans. Amer. Math. Soc. 174 (1972), 333-344
MSC: Primary 34B25
MathSciNet review: 0328189
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Abstract: We investigate the extent to which the eigenfunction expansions arising from a large class of two-point boundary value problems behave like Fourier series expansions in the norm of $ {L^p}(0,1),1 < p < \infty $. We obtain our results by relating Green's function to the Hilbert transform.

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Keywords: Two-point boundary value problem, eigenfunction expansions, Green's function, asymptotic estimates, Hilbert transform
Article copyright: © Copyright 1972 American Mathematical Society