Related papers: Calcul de Wick en dimension infinie

Assuming a lower bound on the dimension, we prove a long standing conjecture concerning the classification of global solutions of the obstacle problem with unbounded coincidence sets.

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

We prove a sharp upper bound on convex domains, in terms of the diameter alone, of the best constant in a class of weighted Poincar\'e inequalities. The key point is the study of an optimal weighted Wirtinger inequality.

Let $K$ be a number field, and let $W$ be a subspace of $K^N$, $N \geq 1$. Let $V_1,...,V_M$ be subspaces of $K^N$ of dimension less than dimension of $W$. We prove the existence of a point of small height in $W \setminus \bigcup_{i=1}^M…

We establish the strong L2(P)-convergence of properly rescaled Wick powers as the power index tends to infinity. The explicit representation of such limit will also provide the convergence in distribution to normal and log-normal random…

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

This short paper gives another proof of the infinitude of primes by using upper box dimension, which is one of fractal dimensions.

We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.

We determine the finite groups whose real irreducible representations have different degrees.

We prove, under suitable conditions, a lower bound on the number of pinned distances determined by small subsets of two-dimensional vector spaces over fields. For finite subsets of the Euclidean plane we prove an upper bound for their…

We prove a rigidity result for Serrin's overdetermined problem in a cone that is contained in a half-space in arbitrary dimensions. In the special case where the cone is an epigraph, this result was shown previously in low dimensions with a…

We extend the Law of Sines to simplices in Euclidean spaces of any number of dimensions.

We provide infinitely many solutions of a Dirichlet problem on balls.

We present a proof of an upper bound for the lengths of finite dimensional representations of algebras obeying a modified PBW property, including Lie algebras and quantum groups. The sharpness of the bound is proved and discussed.

We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.

Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.

We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of…

We prove an optimal lower bound for the best constant in a class of weighted anisotropic Poincar\'e inequalities

We prove finiteness results on integral points on complements of large divisors in projective varieties over finitely generated fields of characteristic zero. To do so, we prove a function field analogue of arithmetic finiteness results of…