Related papers: Short Hardy fields

It has been shown that space-time coordinates can exhibit only very few types of short-distance structures, if described by linear operators: they can be continuous, discrete or "unsharp" in one of two ways. In the literature, various…

We establish Hardy--Littlewood inequalities for the Heckman--Opdam transform associated to a general root datum $(\mathfrak{a},\Sigma,m)$ that generalizes an analogous result for the spherical Fourier transform on a Riemannian symmetric…

We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…

Ellenberg, Venkatesh, and Westerland have established a weak form of the function field analogue of the Cohen--Lenstra heuristic, on the distribution of imaginary number fields with $\ell$-parts of their class groups isomorphic to a fixed…

The subject of this PhD thesis is harmonic analysis on solvable extensions of H-type groups. Let N be an H-type group and S=NA be its solvable extension of rank one. The author study the weak type 1 boundedness of suitable Hardy-Littlewood…

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…

The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic…

The present article surveys surreal numbers with an informal approach, from their very first definition to their structure of universal real closed analytic and exponential field. Then we proceed to give an overview of the recent…

We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions…

Wedderburn showed in 1905 that finite fields are commutative. As for infinite fields, we know that superstable (Cherlin, Shelah) and supersimple (Pillay, Scanlon, Wagner) ones are commutative. In their proof, Cherlin and Shelah use the fact…

We compute the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional Lie algebra by using only properties of the adjoint representation and its dual. We explicitly compute the…

We introduce a technique relying on the use of auxiliary fields in order to eliminate explicit field-derivatives that plague the high orders renormalization group treatment of shift-symmetric, derivative, theories. This technique simplifies…

Let $q$ be a quadratic form over a field $F$ and let $L$ be a field extension of $F$ of odd degree. It is a classical result that if $q_L$ is isotropic (resp. hyperbolic) then $q$ is isotropic (resp. hyperbolic). In turn, given two…

We define nonassociative cyclic extensions of degree m of both fields and central simple algebras over fields. If a suitable field contains a primitive mth (resp., qth) root of unity, we show that suitable nonassociative generalized cyclic…

The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give…

In models of (non-relativistic and pseudo-relativistic) electrons interacting with static nuclei and with the (ultraviolet-cutoff) quantized radiation field, the existence of asymptotic electromagnetic fields is established. Our results…

We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space $H^2$ on the unit disc. This answers a question posed by Shapiro and Sundberg in 1990. We also establish…

Let $L= - \mathrm{div} (A \nabla \cdot)$ be an elliptic operator defined on an open subset of $\mathbb{R}^d$, complemented with mixed boundary conditions. Under suitable assumptions on the operator and the geometry, we derive an atomic…

In this paper we introduce a notion of magnetic field in the Heisenberg group and we study its influence on spectral properties of the corresponding magnetic (sub-elliptic) Laplacian. We show that uniform magnetic fields uplift the bottom…

We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a…