Abstract. We generalize the classical Muckenhoupt inequality with two measures to three under appropriate conditions. As a consequence, we prove a simple characterization of the boundedness of the multiplication operator and thus of the boundedness of the zeros and the asymptotic behavior of the Sobolev orthogonal polynomials, for a large class of measures which includes the most usual examples...

We construct a measure such that if {pn(z)} is the sequence of orthogonal polynomials relative to that measure, then the Riemann Hypothesis with simple zeros is true if and only if limn→∞ p2n(z) p2n(0) = (1/2+iz) (1/2) where (s)= 1 2 s(s − 1) −s/2 (s/2) (s) is the Riemann -function. © 2005 Elsevier Inc. All rights reserved.

For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we study the zeros and poles of the quantum current operators and present a condition of integrability on the quantum current of Uq ( ŝl(2) ) , which is a deformation of the corresponding condition for ŝl(2).

The nearest singular polynomials to a given polynomial have been studied in [1], based on minimization of quadratic forms. An equivalent expression of the quadratic form is presented. It leads to a simple equation satisfied by the double zeros of the nearest singular polynomials. The amount of computational work is economized.

We derive the large n asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the nth section of the exponential sum into “genuine zeros,” which approach, as n → ∞, the zeros of the exponential sum, and “spurious zeros,” which go to infinity as n → ∞. We show that the spurious zeros, after scaling down by the factor of n, approach a “rosette,” a finite collecti...

We use the method of interlacing families polynomials to derive a simple proof Bourgain and Tzafriri’s Restricted Invertibility Principle, then sharpen result in two ways. show that stable rank can be replaced by Schatten 4-norm tighter bounds hold when number columns matrix under consideration does not greatly exceed its rows. Our are derived from an analysis smallest zeros Jacobi associated L...

The notions of decoupling zeros of positive discrete-time linear systems are introduced. The relationships between the decoupling zeros of standard and positive discrete-time linear systems are analyzed. It is shown that: 1) if the positive system has decoupling zeros then the corresponding standard system has also decoupling zeros, 2) the positive system may not have decoupling zeros when the ...

A two-player game is sparse if most of its payoff entries are zeros. We show that the problem of computing a Nash equilibrium remains PPAD-hard to approximate in fully polynomial time for sparse games. On the algorithmic side, we give a simple and polynomial-time algorithm for finding exact Nash equilibria in a class of sparse win-lose games.

First we give here a simple proof of a remarkable result of Videnskii and Shirokov: let B be a Blaschke product with n zeros, then there exists an outer function φ, φ(0) = 1, such that ‖(Bφ)′‖ ≤ Cn, where C is an absolute constant. Then we apply this result to a certain problem of finding the asymptotic of orthogonal polynomials.

the aim of this note is to characterize the finite groups in which all non-linear irreducible characters have distinct zero entries number.