Regularity estimates for an integral operator with a symmetric continuous kernel on convex bounded domain are derived. The covariance of mean-square random field the is example such operator. form Hilbert--Schmidt norms and its square root, composed fractional powers elliptic equipped homogeneous boundary conditions either Dirichlet or Neumann type. These types estimates, which couple regularit...

In this article we obtain estimates on the approximate eigenstructure of channels with a spreading function supported only on a set of finite measure |U |. Because in typical application like wireless communication the spreading function is a random process corresponding to a random Hilbert–Schmidt channel operator H we measure this approximation in terms of the ratio of the p–norm of the devia...

Finite-dimensional harmonic models for theH2 norm evaluation of finitedimensional linear continuous-time periodic (FDLCP) systems are derived, which are expressed explicitly through finitely many Fourier coefficients of the system matrices, and thus dispense with the transition matrix knowledge of any FDLCP models, as opposed to most existing methods in the literature. This paper also shows tha...

Let Xi denote free identically-distributed random variables. This paper investigates how the norm of products Πn = X1X2...Xn behaves as n approaches infinity. In addition, for positive Xi it studies the asymptotic behavior of the norm of Yn = X1 ◦ X2 ◦ ... ◦ Xn, where ◦ denotes the symmetric product of two positive operators: A ◦B =: ABA. It is proved that if the expectation of Xi is 1, then th...

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...

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...