Related papers: Compensated Compactness, Separately convex Functio…

In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foias, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative…

Let $\nu\in [-1/2,\infty)^n$, $n\ge 1$, and let $\mathcal{L}_\nu$ be a self-adjoint extension of the differential operator \[ L_\nu := \sum_{i=1}^n \left[-\frac{\partial^2}{\partial x_i^2} + x_i^2 + \frac{1}{x_i^2}(\nu_i^2 -…

In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…

Let M be a II_1 factor, A a masa in M and E the unique conditional expectation on A. Under some technical assumptions on the inclusion of A in M, which hold true for any semiregular masa of a separable factor, we show that for every…

In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and we provide a priori error estimates for them. The abstract analysis is exemplified by…

We study optimal transportation of measures on compact manifolds for costs defined from convex Lagrangians. We prove that optimal transportation can be interpolated by measured Lipschitz laminations, or geometric currents. The methods are…

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…

In [5] I.P. Goulden, D.M. Jackson, and R. Vakil formulated a conjecture relating certain Hurwitz numbers (enumerating ramified coverings of the sphere) to the intersection theory on a conjectural Picard variety. We are going to use their…

A complete classification of all zonal, continuous, and translation invariant valuations on convex bodies is established. The valuations obtained are expressed as principal value integrals with respect to the area measures. The convergence…

We show that compactly supported wavelets in L^2(R) of scale N may be effectively parameterized with a finite set of spin vectors in C^N, and conversely that every set of spin vectors corresponds to a wavelet. The characterization is given…

We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to…

The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…

Let $(W,S)$ be a Coxeter system whose graph is connected, with no infinite edges. A self-map $\tau$ of $W$ such that $\tau_{\sigma\theta}\in \{\tau_{\theta},\ \sigma\tau_{\theta}\}$ for all $\theta\in W$ and all reflections $\sigma$…

We establish universality of the renormalised energy for mappings from a planar domain to a compact manifold, by approximating subquadratic polar convex functionals of the form $\int_\Omega f(|\mathrm{D} u|)\,\mathrm{d} x$. The analysis…

A \Riesz-basis sequence for $L_2[-\pi,\pi]$ is a strictly increasing sequence $X:=(x_j)_{j\in\mathbb{Z}}$ in $\mathbb{R}$ such that the set of functions $\left(e^{-ix_j(\cdot)}\right)_{j\in\mathbb{Z}}$ is a Riesz basis for $L_2[-\pi,\pi]$.…

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

We prove various estimates for the asymptotics of counting functions associated to point sets of coherent frames and Riesz sequences. The obtained results recover the necessary density conditions for coherent frames and Riesz sequences for…

Using recent work of Bourgain-Dyatlov we show that for any convex co-compact hyperbolic surface Strichartz estimates for the Schr\"odinger equation hold with an arbitrarily small loss of regularity.

We obtain a Bochner type formula and an estimate from below on the spectrum of the sublaplacian of a compact strictly pseudoconvex CR manifold.

We prove interpolating estimates providing a bound for the oscillation of a function in terms of two $L^p$ norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient.…