Normes -adiques et extensions quadratiques
On classifie les orbites de sur l’immeuble de Bruhat-Tits de pour trois paires sphériques de groupes -adiques classiques.
On the product theory of singular integrals.
We establish Lp-boundedness for a class of product singular integral operators on spaces M = M1 x M2 x . . . x Mn. Each factor space Mi is a smooth manifold on which the basic geometry is given by a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type. The standard singular integrals on Mi are non-isotropic smoothing operators of order zero. The boundedness of the product operators is then a consequence of a natural Littlewood- Paley theory on M. This in...
Periodic harmonic functions on lattices and points count in positive characteristic
This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation, the game “Lights Out” following the work of Sutner [20], Goldwasser- Klostermeyer-Ware [5], Barua-Ramakrishnan-Sarkar [2, 19], Hunzikel-Machiavello-Park [12] e.a.; see also [22, 23] for a more detailed account. Our approach uses harmonic analysis and algebraic geometry over a field of positive characteristic.
Regular quasimultipliers of some semisimple Banach algebras
Regularity of conjugacies between critical circle maps: an experimental study.
Representations of Jordan algebras and special functions
This paper is concerned with the action of a special formally real Jordan algebra U on an Euclidean space E, with the decomposition of E under this action and with an application of this decomposition to the study of Bessel functions on the self-adjoint homogeneous cone associated to U.
Restricting cuspidal representations of the group of automorphisms of a homogeneous tree
Let be a homogeneous tree in which every vertex lies on edges, where . Let be the group of automorphisms of , and let be the its subgroup , where is a local field whose residual field has order . We consider the restriction to of a continuous irreducible unitary representation of . When is spherical or special, it was well known that remains irreducible, but we show that when is cuspidal, the situation is much more complicated. We then study in detail what happens when the...
Sur les intégrales d'entrelacement de R. A. Kunze et E. M. Stein
The Green formula and HP Spaces on trees.
The Pick problem and the Cole-Lewis-Wermer theorem.
The Pick problem in and and the Cole-Lewis-Wermer problem.
The structure of the Haar systems on locally compact groupoids.
Triebel-Lizorkin spaces with non-doubling measures
Suppose that μ is a Radon measure on , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality...
Type-dependent positive definite functions on free products of groups
Дзета-функция трансверсально эллиптического оператора.
О голоморфном продолжении -гиперфункций в фиксированную область.
Об экстремальных инвариантных пространствах.