Related papers: Optimal bounds for the Dunkl kernel in the dihedra…

We produce precise estimates for the Kogbetliantz kernel for the approximation of functions on the sphere. Furthermore, we propose and study a new approximation kernel, which has slightly better properties.

We study the duality of moduli of k- and (n-k)-dimensional slices of euclidean n-cubes, and establish the optimal upper bound 1.

In this paper necessary and sufficient conditions are presented for heat kernel upper bounds for random walks on weighted graphs. Several equivalent conditions are given in the form of isoperimetric inequalities.

For two decades, reproducing kernels and their associated discrepancies have facilitated elegant theoretical analyses in the setting of quasi Monte Carlo. These same tools are now receiving interest in statistics and related fields, as…

We construct maximal $\Lambda(p)$-subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.

We survey the known results regarding the boundaries of word-hyperbolic groups.

In this article we establish the optimal $C^s$ boundary regularity for solutions to nonlocal parabolic equations in divergence form in $C^{1,\alpha}$ domains and prove a higher order boundary Harnack principle in this setting. Our approach…

We obtain the sharp lower bound for the uniform norm of the orthogonal polynomials in the Steklov class. We also prove the sharp estimates for the polynomial entropy in this class.

We prove on-diagonal bounds for the heat kernel of the Dirichlet Laplacian $-\Delta^D_\Omega$ in locally twisted three-dimensional tubes $\Omega$. In particular, we show that for any fixed $x$ the heat kernel decays for large times as…

In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.

We study the $2k$-th moment of central values of the family of Dirichlet $L$-functions to a fixed prime modulus and establish sharp upper bounds for all real $k \in [0,2]$.

Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials.…

It was conjectured that the augmentation ideal of a dihedral quandle of even order $n>2$ satisfies $|\Delta^k(\text{R}_n)/\Delta^{k+1}(\text{R}_{n})|=n$ for all $k\geq 2$. In this article we provide a counterexample against this conjecture.

In this note, pointwise best-possible (lower and upper) bounds on the set of copulas with a given value of the Gini's gamma coefficient are established. It is shown that, unlike the best-possible bounds on the set of copulas with a given…

We prove a lower bound on the dimension of the set of maximal border subrank tensors. This is the first such bound of its type.

Heavy quarks, namely, the top and bottom quarks, may show great sensitiveness to new physics effects. In particular, they might have unusually large electric dipole moments. This possibility is analyzed via the corresponding one-loop…

We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…

We show that the maximum slope invariant for tubular groups is easy to calculate, and give an example of two tubular groups that are distinguishable by their maximum slopes but not by edge pattern considerations or isoperimetric function.

We extend approximate next-to-next-to-leading order results for top-pair production to include the semi-leptonic decays of top quarks in the narrow-width approximation. The new hard-scattering kernels are implemented in a fully differential…

In this thesis we describe a type of metric space called an Euclidean polyhedral complex. We define a Dirichlet form on it; this is used to give a corresponding heat kernel. We provide a uniform small time Poincare inequality for complexes…