On a family of integral operators of Hankel type
In the paper under review, the author considers a family of integral Hankel operators \(K^{(j)}\), \(j\geq0\), on \(L^2(0,\infty)\). The operator \(K_j\) is unitarily equivalent to the Hankel operator on the Hardy class \(H^2\) on the unit circle \({\mathbb T}\) with symbol \(2z^{j+1}\chi\), where \(\chi\) is the characteristic function of the right half-circle \(\{\zeta\in{\mathbb T}:\text{Re}\zeta\geq0\}\). The author performs explicit diagonalizations of the operators \(K^{(j)}\) and proves that each \(K^{(j)}\) has simple absolutely continuous spectrum filling \([-1,1]\).
scientific article; zbMATH DE number 6199460
scientific article