Related papers: The Bounded Spherical Functions on the Cartan moti…
We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients.…
In this paper, we define edge zeta functions for spherical buildings associated with finite general linear groups. We derive elegant formulas for these zeta functions and reveal patterns of eigenvalues of these buildings, by introducing and…
In this paper we deal with lacunary and full versions of the spherical maximal function on the Heisenberg group $\mathbb{H}^n$, for $n\ge 2$. By suitable adaptation of an approach developed by M. Lacey in the Euclidean case, we obtain…
We study the automorphisms group action on a bounded domain in $\CC^n$ having a boundary point that is exponentially flat. Such a domain typically has a compact automorphism group. Our results enable us to generate many new examples.
We write a generating function for all spherical functions on the product of several copies of SU(2).
We construct Brownian motion on a wide class of metric spaces similar to graphs, and show that its cover time admits an upper bound depending only on the length of the space.
We prove that the Dehn function of a group of Stallings that is finitely presented but not of type F_3 is quadratic. To appear in Geometric and Functional Analysis.
A treatment is given of the orbit dynamics for linear unstable motion that allows for the zeros in the beta function and makes no assumptions about the realness of the betatron and phase functions. The phase shift per turn is shown to be…
We consider $\mathbb{R}^3$ as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary $\tau\in \widehat{SO(3)}$, let $E_\tau$ be the homogeneous vector bundle over $\mathbb{R}^3$…
More precise estimates for the Bergman metric on strongly pseudoconvex domains are given, based on the use of the squeezing function.
It is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.
For a domain $\Omega\subset\mathbb R^n$, we introduce the concept of a uniformly $C^m$ defining function. We characterize uniformly $C^m$ defining functions in terms of the signed distance function for the boundary and provide a large class…
We identify a class of continuous compactly supported functions for which the known part of the Gabor frame set can be extended. At least for functions with support on an interval of length two, the curve determining the set touches the…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
We consider the spherical variety of quadratic forms over a quadratically closed field of characteristic 2, and determine its orbits for the action of the Borel subgroup of upper triangular matrices. We exhibit a connection between these…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
We establish a boundary Harnack principle for a large class of subordinate Brownian motion, including mixtures of symmetric stable processes, in bounded $\kappa$-fat open set (disconnected analogue of John domains). As an application of the…
A Lieb-Thirring bound for Schr\"odinger operators with Bernstein functions of the Laplacian is shown by functional integration techniques. Several specific cases are discussed in detail.
We consider the averages of a function $ f$ on $ \mathbb R ^{n}$ over spheres of radius $ 0< r< \infty $ given by $ A_{r} f (x) = \int_{\mathbb S ^{n-1}} f (x-r y) \; d \sigma (y)$, where $ \sigma $ is the normalized rotation invariant…
In this article, we study weighted estimates for a general class of lacunary maximal functions on homogeneous groups. As an application we derive improved weighted estimates for the lacunary maximal function associated to the Kor\'anyi…