Results 1  10
of
24
New bounds on the LiebThirring constants
 Invent. Math
"... ABSTRACT. Improved estimates on the constants Lγ,d, for 1/2 < γ < 3/2, d ∈ N in the inequalities for the eigenvalue moments of Schrödinger operators are established. 1. ..."
Abstract

Cited by 17 (8 self)
 Add to MetaCart
ABSTRACT. Improved estimates on the constants Lγ,d, for 1/2 < γ < 3/2, d ∈ N in the inequalities for the eigenvalue moments of Schrödinger operators are established. 1.
MIMO diversity in the presence of double scattering
 IEEE Trans. Inform. Theory
, 2008
"... The potential benefits of multipleantenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multipleinput multipleoutput (MIMO) syste ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
The potential benefits of multipleantenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multipleinput multipleoutput (MIMO) systems, with an emphasis on orthogonal space–time block codes, in terms of the symbol error probability, the effective fading figure (EFF), and the capacity at low signaltonoise ratio (SNR). In particular, we consider a general family of MIMO channels known as doublescattering channels, which encompasses a variety of propagation environments from independent and identically distributed Rayleigh to degenerate keyhole or pinhole cases by embracing both rankdeficient and spatial correlation effects. It is shown that a MIMO system with nT transmit and nR receive antennas achieves the diversity of order nTnSnR max(nT,nS,nR) in a doublescattering channel with nS effective scatterers. We also quantify the combined effect of the spatial correlation and the lack of scattering richness on the EFF and the lowSNR capacity in terms of the correlation figures of transmit, receive, and scatterer correlation matrices. We further show the
A general approach to sparse basis selection: Majorization, concavity, and affine scaling
 IN PROCEEDINGS OF THE TWELFTH ANNUAL CONFERENCE ON COMPUTATIONAL LEARNING THEORY
, 1997
"... Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schurconcavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures use ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schurconcavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and several general classes of measures are proposed and analyzed in this paper. Admissible measures are given by the Schurconcave functions, which are the class of functions consistent with the socalled Lorentz ordering (a partial ordering on vectors also known as majorization). In particular, concave functions form an important subclass of the Schurconcave functions which attain their minima at sparse solutions to the best basis selection problem. A general affine scaling optimization algorithm obtained from a special factorization of the gradient function is developed and proved to converge to a sparse solution for measures chosen from within this subclass.
SPECTRAL ORDER AND ISOTONIC DIFFERENTIAL OPERATORS OF LAGUERREPÓLYA TYPE
, 2004
"... Abstract. The spectral order on R n induces a natural partial ordering on the manifold Hn of monic hyperbolic polynomials of degree n. We show that all differential operators of LaguerrePólya type preserve the spectral order. We also establish a global monotony property for infinite families of def ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
Abstract. The spectral order on R n induces a natural partial ordering on the manifold Hn of monic hyperbolic polynomials of degree n. We show that all differential operators of LaguerrePólya type preserve the spectral order. We also establish a global monotony property for infinite families of deformations of these operators parametrized by the space l ∞ of real bounded sequences. As a consequence, we deduce that the monoid A ′ of linear operators that preserve averages of zero sets and hyperbolicity consists only of differential operators of LaguerrePólya type which are both extensive and isotonic. In particular, these results imply that any hyperbolic polynomial is the global minimum of its A ′orbit and that Appell polynomials are characterized by a global minimum property with respect to the spectral order.
Optimal reconstruction systems for erasures and the qpotential, preprint
"... Abstract. We introduce the qpotential as an extension of the BenedettoFickus frame potential, defined on general reconstruction systems and we show that protocols are the minimizers of this potential under certain restrictions. We extend recent results of B.G. Bodmann on the structure of optimal p ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract. We introduce the qpotential as an extension of the BenedettoFickus frame potential, defined on general reconstruction systems and we show that protocols are the minimizers of this potential under certain restrictions. We extend recent results of B.G. Bodmann on the structure of optimal protocols with respect to 1 and 2 lost packets where the worst (normalized) reconstruction error is computed with respect to a compatible unitarily invariant norm. We finally describe necessary and sufficient (spectral) conditions, that we call qfundamental inequalities, for the existence of protocols with prescribed properties by relating this problem to Klyachko’s and Fulton’s theory on sums of hermitian operators.
Radjabalipuor,The structure of linear operators strongly preserving majorizations of matrices
 Electronic Journal of Linear Algebra
"... Abstract. A matrix majorization relation A ≺r B (resp., A ≺ℓ B) on the collection Mn of all n × n real matrices is a relation A = BR (resp., A = RB) forsomen × n row stochastic matrix R (depending on A and B). These right and left matrix majorizations have been considered by some authors under the n ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract. A matrix majorization relation A ≺r B (resp., A ≺ℓ B) on the collection Mn of all n × n real matrices is a relation A = BR (resp., A = RB) forsomen × n row stochastic matrix R (depending on A and B). These right and left matrix majorizations have been considered by some authors under the names “matrix majorization ” and “weak matrix majorization, ” respectively. Also, a multivariate majorization A ≺rmul B (resp., A ≺ℓmul B) isarelationA = BD (resp., A = DB) forsomen × n doubly stochastic matrix D (depending on A and B). The linear operators T: Mn → Mn which strongly preserve each of the above mentioned majorizations are characterized. Recall that an operator T: Mn → Mn strongly preserves a relation R on Mn when R(T (X),T(Y)) if and only if R(X, Y). The results are the sharpening of wellknown representations TX = CXD or TX = CXtD for linear operators preserving invertible matrices.
Minimization of convex functionals over frame operators
 Adv. Comput. Math
"... Abstract. We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the BenedettoFickus frame potential. Our approach depends on majorization techniques. We also consider some perturb ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Abstract. We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the BenedettoFickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator of a set of vectors is realized as the frame operator of a set of vectors which is close to the original one. 1.
The local form of doubly stochastic maps and joint majorization in II1 factors
 Integral Equations Operator Theory
, 2008
"... Dedicated to our families Abstract. We find a description of the restriction of doubly stochastic maps to separable abelian C ∗subalgebras of a II1 factor M. We use this local form of doubly stochastic maps to develop a notion of joint majorization between ntuples of mutually commuting selfadjoin ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Dedicated to our families Abstract. We find a description of the restriction of doubly stochastic maps to separable abelian C ∗subalgebras of a II1 factor M. We use this local form of doubly stochastic maps to develop a notion of joint majorization between ntuples of mutually commuting selfadjoint operators that extends those of Kamei (for single selfadjoint operators) and Hiai (for single normal operators) in the II1 factor case. Several characterizations of this joint majorization are obtained. As a byproduct we prove that any separable abelian C ∗subalgebra of M can be embedded into a separable abelian C ∗subalgebra of M with diffuse spectral measure. 1.
A MATRIX INTERPOLATION BETWEEN CLASSICAL AND FREE MAX OPERATIONS. I. THE
, 806
"... Abstract. Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two independent random variables. We present here a new insight on this analogy: its concrete realization based on r ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two independent random variables. We present here a new insight on this analogy: its concrete realization based on random matrices giving an interpolation between classical and free settings. Contents
THE STRUCTURE OF LINEAR PRESERVERS OF LEFT MATRIX MAJORIZATION ON RP ∗
"... Abstract. For vectors X, Y ∈ Rn, Y is said to be left matrix majorized by X (Y ≺ℓ X) if for some row stochastic matrix R, Y = RX. A linear operator T: Rp → Rn is said to be a linear preserver of ≺ℓ if Y ≺ℓ X on Rp implies that TY ≺ℓ TX on Rn. The linear operators T: Rp → Rn (n
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract. For vectors X, Y ∈ Rn, Y is said to be left matrix majorized by X (Y ≺ℓ X) if for some row stochastic matrix R, Y = RX. A linear operator T: Rp → Rn is said to be a linear preserver of ≺ℓ if Y ≺ℓ X on Rp implies that TY ≺ℓ TX on Rn. The linear operators T: Rp → Rn (n <p(p−1)) which preserve ≺ℓ have been characterized. In this paper, linear operators T: Rp → Rn which preserve ≺ℓ are characterized without any condition on n and p.