Periodic “weighted” operators

Weighted slant Toep-Hank Operators

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

Parametrization of Periodic Weighted Operators in Terms of Gap Lengths

We consider the periodic weighted operator T y = ? ?2 (2 y 0) 0 in L 2 (R; (x) 2 dx), where is a 1-periodic real positive function with (0) = 1. We assume q = 0 == 2 L 2 (0; 1). The spectrum of T consists of intervals n = + n?1 ; ? n ] separated by gaps (? n ; + n); n > 1. Using essentially the square of the gap lengths, the centre of the gap and the Dirichlet eigenvalues on the unit interval w...

Weighted Frobenius-Perron and Koopman operators

On reducibility of weighted composition operators

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

Weighted composition operators on weighted Bergman spaces and weighted Bloch spaces

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.