We affirmatively settle the question on existence of a real-valued higher order spectral shift function for pair self-adjoint operators $H$ and $V$ such that is bounded $V(H-iI)^{-1}$ belongs to Schatten–von Neumann ideal $\mathcal{S}^n$ compact in separable Hilbert space. also show satisfies same trace formula as known case $V\in\mathcal{S}^n$ it unique up polynomial summand $n-1$. Our result ...

In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathca...

We study a new class of structured Schatten norms for tensors that includes two recently proposed norms (“overlapped” and “latent”) for convex-optimization-based tensor decomposition. Based on the properties of the structured Schatten norms, we analyze the performance of “latent” approach for tensor decomposition, which was empirically found to perform better than the “overlapped” approach in s...

let $g$ be a locally compact group, $h$ be a compact subgroup of $g$ and $varpi$ be a representation of the homogeneous space $g/h$ on a hilbert space $mathcal h$. for $psi in l^p(g/h), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $l_{psi,zeta} $ on $mathcal h$ and we show that it is a bounded operator. moreover, we prove that the localizat...

We study time-frequency localization operators of the form A12 a , where a is the symbol of the operator and φ1, φ2 are the analysis and synthesis windows, respectively. It is shown in [3] that a sufficient condition for A12 a ∈ Sp(L(R)), the Schatten class of order p, is that a belongs to the modulation space Mp,∞(R2d) and the window functions to the modulation space M1. Here we prove a partia...

A compactness criterion for Stieltjes transformation S λ : L 2 → L 2 of the form (1.1) is obtained. The main result is conditions for belonging S λ to Schatten-von Neumann class S p , 0 < p < ∞.