The Eigenfunctions of the Hilbert Matrix
For each noninteger complex number lambda, the Hilbert matrix H-lambda = (1/n+m+lambda)(n,m >= 0) defines a bounded linear operator on the Hardy spaces H-p, 1 < p < a, and on the Korenblum spaces , A(-tau), tau > 0. In this work, we determine the point spectrum with multiplicities of the Hilbert matrix acting on these spaces. This extends to complex lambda results by Hill and Rosenblum for real la