k=1 |ak|. Hardy’s inequality can be interpreted as the lp operator norm of the Cesàro matrix C, given by cj,k = 1/j, k ≤ j, and 0 otherwise, is bounded on lp and has norm ≤ p/(p − 1) (The norm is in fact p/(p − 1)). It is known that the Cesàro operator is not bounded below, or the converse of inequality (1.1) does not hold for any positive constant. However, if one assumes C acting only on non-...

Standard Principal-Component Analysis (PCA) is known to be very sensitive to outliers among the processed data. On the other hand, in has been recently shown that L1-norm-based PCA (L1-PCA) exhibits sturdy resistance against outliers, while it performs similar to standard PCA when applied to nominal or smoothly corrupted data. Exact calculation of the K L1-norm Principal Components (L1-PCs) of ...

k=1 |ak| . Hardy’s inequality can be interpreted as the lp operator norm of the Cesàro matrix C, given by cj,k = 1/j, k ≤ j, and 0 otherwise, is bounded on l p and has norm ≤ p/(p − 1) (The norm is in fact p/(p − 1)). It is known that the Cesàro operator is not bounded below, or the converse of inequality (1.1) does not hold for any positive constant. However, if one assumes C acting only on no...

We analyze the convergence of a discontinuous Galerkin method (DGM) with plane waves and Lagrange multipliers that was recently proposed by Farhat et al. [3] for solving twodimensional Helmholtz problems at relatively high wave numbers. We prove that the underlying hybrid variational formulation is well-posed. We also present various a priori error estimates that establish the convergence and o...

The paper contains three results, the common feature of which is that they deal with the Schatten p class. The first is a presentation of a new complemented subspace of Cp in the reflexive range (and p ̸= 2). This construction answers a question of Arazy and Lindestrauss from 1975. The second result relates to tight embeddings of finite dimensional subspaces of Cp in C n p with small n and shows...

The covering radius R of a code is the maximal distance of any vector from the code. This work gives a number of new results concerning t[ n, k], the minimal covering radius of any binary code of length n and dimension k. For example r[ n, 41 and t [ n, 51 are determined exactly, and reasonably tight bounds on t[ n, k] are obtained for any k when n is large. These results are found by using sev...

A type of oscillation modeled on BMO is introduced to characterize norm compactness in L 1. This result is used to characterize the bounded linear operators from L 1 into a Banach space X that map weakly convergent sequences onto norm convergent sequences (i.e. are Dunford-Pettis). This characterization is used to study the geometry of Banach spaces X with the property that all bounded linear o...

Low-rank factorization is used in many areas of computer science where one performs spectral analysis on large sensitive data stored in the form of matrices. In this paper, we study differentially private low-rank factorization of a matrix with respect to the spectral norm in the turnstile update model. In this problem, given an input matrix A ∈ Rm×n updated in the turnstile manner and a target...