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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0328189-0
PII: S 0002-9947(1972)0328189-0
Keywords: Two-point boundary value problem, eigenfunction expansions, Green's function, asymptotic estimates, Hilbert transform
Article copyright: © Copyright 1972 American Mathematical Society