The 𝐿^{𝑝} behavior of eigenfunction expansions

Benzinger, Harold E.

doi:10.1090/S0002-9947-1972-0328189-0

The $L^{p}$ behavior of eigenfunction expansions
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Trans. Amer. Math. Soc. 174 (1972), 333-344 Request permission

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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Linear operators

Linear differential operators

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