In this paper we study Toeplitz and Cesàro-type operators on holomorphic function spaces a homogeneous Siegel domain of Type II. We prove several necessary conditions sufficient for these to be continuous or compact, belong suitable Schatten classes.

In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The are given in terms of spectral properties acting on kernel. As applications several criteria different types differential and their asymptotics settings: compact manifolds, lattices, domains Rn finite measure, for anharmonic oscillators. We also give e...

A Helson matrix is an infinite $A = (a_{m,n})_{m,n\geq1}$ such that the entry $a_{m,n}$ depends only on product $mn$. We demonstrate orthogonal projection from Hilbert--Schmidt class $\mathcal{S}_2$ onto subspace of matrices does not extend to a bounded operator Schatten $\mathcal{S}_q$ for $1 \leq q \neq 2 < \infty$. In fact, we prove more general result showing large natural projections are u...