The 𝐿^{𝑝} behavior of eigenfunction expansions
Harold E. Benzinger · Transactions of the American Mathematical Society · 1972
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 > ∞ {L^p}(0,1),1 > p > \infty . We obtain our results by relating Green’s function to the Hilbert transform.