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We obtain new mixed-norm estimates and geometric results on projections. In the proof we introduce a new quantity called s-amplitude, and interpolate analytically not only on p,q, but also on dimensio...
Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N. Normalize the hyperbolic measure such that vol(Y0(N)) = 1 and the form f such that kfk2 = 1. It is shown that kfk1 ≪1...
We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has first been found for nonparametric regression and for signal estimation in Gaussian ...
The minimum `1-norm solution to an underdetermined system of linear equations y = Ax, is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest i...
We consider inexact linear equations y ≈ Φα where y is a given vector in R n , Φ is a given n by m matrix, and we wish to find an α0, which is sparse and gives an approximate solution, obey...
We consider linear equations y = Φα where y is a given vector in R n , Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ Rm. We suppose that the columns of Φ are normalized ...
The standard 2-norm SVM is known for its good performance in twoclass classification. In this paper, we consider the 1-norm SVM. We argue that the 1-norm SVM may have some advantage over the standard ...
Inspired by recent work of Byers we establish a simple connection between the singular values of a transfer matrix evaluated along the imaginary axis and the imaginary eigenvalues of a related Hamilto...
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
For linear systems that contain unspecified parameters that lie in given intervals, we present a branch and bound algorithm for computing the maximum H_infinity-norm over the set of uncertain paramete...
We consider a stationary solution of the Poisson equation (λ − Lω)φλ(x; ω) = −∂∗b(x; ω), where λ > 0 and Lω is a random, discrete, elliptic operator given by Lωu(x) := ∂&...
We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = Xβ + z, then we ...
In this paper we propose a method associated with an algorithm for generating uniformly scattered points on the the Lp-norm unit sphere and discuss its applications in statistical simulation, repres...
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ...

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