Restriction theorems for Hankel operators

Abstract

We consider a class of maps from integral Hankel operators to Hankel matrices, which we call restriction maps. In the simplest case, such a map is simply a restriction of the integral kernel onto integers. More generally, it is given by an averaging of the kernel with a sufficiently regular weight function. We study the boundedness of restriction maps with respect to the operator norm and the Schatten norms.Of course, for this operation to make sense, the kernel function a has to be continuous. Here is our first result; we denote by S p , 0 < p < ∞, the standard Schatten class of compact operators (see Section 2).

On finite sections of the multiplicative Hilbert inequalities

“…Note that the multiplicative Hilbert matrix is the matrix representation of the integral operator with respect to the basis (n −s ) n 2 for H 2 0 , the Hardy space of Dirichlet series vanishing at +∞ and with square-summable coecients, where ζ is the Riemann zeta function. For a comprehensive study of multiplicative Hilbert matrices, and more generally Helson matrices (also known as multiplicative Hankel matrices), we refer the reader to [6,7,8].…”