In a seminal work, Micciancio & Voulgaris (2010) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus may need exponen ...
We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups ad ...
Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countabl ...
The large sieve inequalities for algebraic trace functions are considered in this article. A fundamental iterative relation is established by classical Fourier analysis, and l-adic Fourier analysis and multiplicative convolutions of sheaves are also requir ...
We prove that a closed subgroup H of a locally compact group G is a set of p-uniqueness (1 < p < infinity) if and only if H is locally negligible. We also obtain the inverse projection theorem for sets of p-uniqueness. ...
This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the ...
We revisit a recent bound of I. Shparlinski and T. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier resul ...
For Figa-Talamanca-Herz algebras A(p)(G), 1 < p < infinity, of a locally compact group G and a closed subgroup H of G, we prove an injection theorem for local Ditkin sets. ...
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric structure of the ...
