We consider the class of integral operators Qφ on L (R+) of the form (Qφf)(x) = ∫ ∞ 0 φ(max{x, y})f(y)dy. We discuss necessary and sufficient conditions on φ to insure that Qφ is bounded, compact, or in the Schatten–von Neumann class Sp, 1 < p < ∞. We also give necessary and sufficient conditions for Qφ to be a finite rank operator. However, there is a kind of cut-off at p = 1, and for membersh...

We give estimates for the approximation numbers of composition operators on H, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approximation numbers are dominated by e−c √ . When the symbol is continuous on the closed unit disk and has a domain touching the boundary non-tangentially at a finite number of points, with a good behavior a...

Both sparse coding and rank minimization have led to great successes in various image processing tasks. Though the underlying principles of these two approaches are similar, no theory is available to demonstrate the correspondence. In this paper, starting by designing an adaptive dictionary for each group of image patches, we analyze the sparsity of image patches in each group using the rank mi...

Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm minimization (NNM) as a convex relaxation of the nonconvex rank minimization. However, NNM tends to over-shrink the rank components and treats the different rank com...

This paper studies the Schatten-q error of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on via projection bound. Then, we lower bounds to justify tightness upper error. further develop user-friendly sin? for subspace based Finally, demonstrate advantage our results over ones in literature simulation.

A countable discrete group is said to be Frobenius stable if every function from the unitary matrices that “almost multiplicative” in norm “close” a representation norm. The purpose of this paper show finitely generated nilpotent groups are not virtually cyclic stable. Our argument proves same result for other unnormalized Schatten p-norms with 1<p≤∞.

This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen generalize recent work Henriksen–Ward, they are similar in spirit to the Ahlswede–Winter Tropp sum The argument relies on uniform smoothness properties Schatten trace classes.

let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

We deduce trace properties for modulation spaces (including certain Wiener-amalgam spaces) of Gelfand–Shilov distributions.We use these results to show that [Formula: see text]dos with amplitudes in suitable spaces, agree normal type whose symbols belong (other) spaces. In particular we extend earlier include quasi-Banach also apply our on Schatten-von Neumann and nuclear