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Completeness of eigenvectors in Banach spaces


Author: Harold E. Benzinger
Journal: Proc. Amer. Math. Soc. 38 (1973), 319-324
MSC: Primary 47A70; Secondary 34B25
DOI: https://doi.org/10.1090/S0002-9939-1973-0318941-6
MathSciNet review: 0318941
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Abstract: We prove a general theorem on the completeness of the eigenvectors of linear operators in a Banach space. We then derive asymptotic estimates for the Green's functions of two-point boundary value problems which allow us to apply the above theorem to a wide class of such problems in the spaces $ {L^p}(0,1),1 \leqq p < \infty $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0318941-6
Article copyright: © Copyright 1973 American Mathematical Society

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