Abstract Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous for product Hilbert spaces. includes, example, the consistency property, i.e. preservation frame property under product, description canonical dual tensors by on space level. show full characterization all systems a given ...

We study when multiplication by a weight can turn non-compact composition operator on \(H^2\) into compact operator, and it be in Schatten classes. The \(q\)-summing case \(H^p\) is considered. also this one.

We study Cwikel-type estimates for the singular values and Schatten Lp-norms of compositions multiplication convolution operators acting on stratified Lie groups. This enables us to obtain novel spectral asymptotic formulas certain derived from sub-Laplacians.

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...