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- Centre National de la Recherche ScientifiqueFR29 papers
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- Pennsylvania State UniversityUS7 papers
- Atlanta Technical CollegeUS6 papers
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6 papers · 1 filter
On the Small Ball Inequality in All Dimensions
Dmitry Bilyk, Michael Lacey, Armen Vagharshakyan
Let h_R denote an L ^{\infty} normalized Haar function adapted to a dyadic rectangle R contained in the unit cube in dimension d. We establish a non-trivial lower bound on the L^{\…
A New Approach to Universality Limits involving Orthogonal Polynomials
Doron S Lubinsky
We show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure mu on [-1,1]. Assume that mu is a r…
Resurgence of the fractional polylogarithms
Ovidiu Costin, Stavros Garoufalidis
The fractional polylogarithms, depending on a complex parameter $\a$, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series i…
On Extensions of a Theorem of Baxter
J. S. Geronimo, A. Martinez-Finkelshtein
We combine the Riemann-Hilbert approach with the techniques of Banach algebras to obtain an extension of Baxter's Theorem for polynomials orthogonal on the unit circle. This is acc…
Factorization of Multivariate Positive Laurent Polynomials
Jeffrey S. Geronimo, Ming-Jun Lai
Recently Dritschel proves that any positive multivariate Laurent polynomial can be factorized into a sum of square magnitudes of polynomials. We first give another proof of the Dri…
Maximal Theorems for the Directional Hilbert Transform on the Plane
Michael T Lacey, Xiaochun Li
For a Schwartz function on the plane and a non-zero $v\in\ZR^2$ define the Hilbert transform of in the direction to be $$ H_vf(x)=\text{p.v.}\int_\ZR f(x-vy) \frac{dy}y…