• Publications
  • Influence
Almost no points on a Cantor set are very well approximable
  • B. Weiss
  • Mathematics
  • Proceedings of the Royal Society of London…
  • 8 April 2001
We prove that almost no numbers in Cantor's middle–thirds set are very well approximable by rationals. More generally, we discuss Diophantine properties of almost every point, where ‘almost every’ isExpand
  • 43
  • 10
On fractal measures and diophantine approximation
We study diophantine properties of a typical point with respect to measures on \(\mathbb{R}^n .\) Namely, we identify geometric conditions on a measure μ on \(\mathbb{R}^n \) guaranteeing thatExpand
  • 72
  • 8
  • PDF
Spatial Aliasing in Spherical Microphone Arrays
TLDR
This paper presents theoretical analysis of spatial aliasing for various sphere sampling configurations, showing how high-order spherical harmonic coefficients are aliased into the lower orders. Expand
  • 156
  • 7
DIRICHLET'S THEOREM ON DIOPHANTINE APPROXIMATION AND HOMOGENEOUS FLOWS
Given an $m \times n$ real matrix $Y$, an unbounded set $\mathcal{T}$ of parameters $t =( t_1, \ldots, t_{m+n})\in\mathbb{R}_+^{m+n}$ with $\sum_{i = 1}^m t_i =\sum_{j = 1}^{n} t_{m+j} $ andExpand
  • 60
  • 7
  • PDF
The automorphism group of the Gaussian measure cannot act pointwise
Classical ergodic theory deals with measure (or measure class) preserving actions of locally compact groups on Lebesgue spaces. An important tool in this setting is a theorem of Mackey which providesExpand
  • 48
  • 7
  • PDF
Chapter 10 – On the Interplay between Measurable and Topological Dynamics
This chapter discusses the interplay between measurable and topological dynamics. Ergodic theory or measurable dynamics and topological dynamic are the two sister branches of the theory of dynamicalExpand
  • 89
  • 6
  • PDF
On fractal measures and diophantine approximation
Abstract.We study diophantine properties of a typical point with respect to measures on $\mathbb{R}^n .$ Namely, we identify geometric conditions on a measure μ on $\mathbb{R}^n $ guaranteeing thatExpand
  • 59
  • 6
THE SET OF BADLY APPROXIMABLE VECTORS IS STRONGLY C 1 INCOMPRESSIBLE
We prove that the countable intersection of C 1 -diffeomorphic images of cer- tain Diophantine sets has full Hausdorff dimension. For example, we show this for the set of badly approximable vectorsExpand
  • 63
  • 6
  • PDF
Closed orbits for actions of maximal tori on homogeneous spaces
Let G be a real algebraic group defined over Q, let 0 be an arithmetic subgroup, and let T be any torus containing a maximal R-split torus. We prove that the closed orbits for the action of T on G/0Expand
  • 44
  • 6
  • PDF
Badly approximable vectors on fractals
For a large class of closed subsetsC of ℝn, we show that the intersection ofC with the set of badly approximable vectors has the same Hausdorff dimension asC. The sets are described in terms ofExpand
  • 63
  • 5
  • PDF