Direction-of-arrival (DOA) estimation is usually confronted with a multiple measurement vector (MMV) case. In this paper, a novel fast sparse DOA estimation algorithm, named the joint smoothed l 0 -norm algorithm, is proposed for multiple measurement vectors in multiple-input multiple-output (MIMO) radar. To eliminate the white or colored Gaussian noises, the new method first obtains a low-comp...

In a linear infinite-dimensional space with scalar product and in finite-dimensional Euclidean the interpolation Hermite polynomial minimal norm, generated by Gaussian measure, contains fundamental polynomials are shown. The accuracy of Hermit’s formulas on appropriate degree researched.

The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymp-totically optimal in order at a growing number of observation on any regular sub-space compactly embedded in space L 2 , and confidence intervals, also adaptive, are constructed on their basis for the estimated functions in an integral norm.

This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Gaussian upper bounds. Math. Z. 260 (2008), no. 3, 527--539

Probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this article we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-ra...

Consider the n-dimensional vector y = Xβ+ ǫ, where β ∈ R has only k nonzero entries and ǫ ∈ R is a Gaussian noise. This can be viewed as a linear system with sparsity constraints, corrupted by noise. We find a non-asymptotic upper bound on the probability that the optimal decoder for β declares a wrong sparsity pattern, given any generic perturbation matrix X . In the case when X is randomly dr...

The Willmore conjecture states that any immersion F : T 2 → Rn of a 2-torus into euclidean space satisfies ∫ T 2 H 2 ≥ 2π2. We prove it under the condition that the Lp-norm of the Gaussian curvature is sufficiently small.

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels.

Gaussian and Chiral β-Ensembles, which generalise well known orthogonal (β = 1), unitary (β = 2), and symplectic (β = 4) ensembles of random Hermitian matrices, are considered. Averages are shown to satisfy duality relations like {β,N, n} ⇔ {4/β, n,N} for all β > 0, where N and n respectively denote the number of eigenvalues and products of characteristic polynomials. At the edge of the spectru...

The purpose of the article is to provide partial proofs for two conjectures given by Witte and Forrester in “Moments of the Gaussian β Ensembles and the large N expansion of the densities” ([1]) with the use of the topological recursion adapted for general β Gaussian case. In particular, the paper uses a version at coinciding points that provides a simple proof for some of the coefficients invo...