Abstract:

We present recent results on spectral properties of the so-called Hilbert L-matrix. First part of the talk is devoted to the semi-infinite matrix operator with a special attention paid to its norm answering open problems raised by L. Bouthat and J. Mashreghi. Second part of the talk concerns asymptotic spectral properties of the finite Hilbert L-matrix for large order. Namely, we study the asymptotic eigenvalue distribution and asymptotic behavior of large and small eigenvalues. In particular, we improve asymptotic formula of H. S. Wilf for the best constant in the finite Hardy inequality.