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

Some weighted inequalities for the maximal operator with respect to the discrete diffusion semigroups associated with exceptional Jacobi and Dunkl-Jacobi polynomials are given. This setup allows to extend the corresponding results obtained…

We give the upper and the lower estimates of heat kernels for Schr\"odinger operators $H=-\Delta+V$, with nonnegative and locally bounded potentials $V$ in $\mathbb{R}^d$, $d \geq 1$. We observe a factorization: the contribution of the…

We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…

We determine a reasonable upper bound for the complexity of collection from the left to multiply two elements of a finite soluble, or polycyclic, group by restricting attention to certain polycyclic presentations of the group.

We establish L^p bounds on L^2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all p between $2 and infinity, up to logarithmic losses…

We establish a lower bound for the representation dimension of all the classical Hecke algebras of types A, B and D. For all the type A algebras, and most of the algebras of types B and D, we also establish upper bounds. Moreover, we…

In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.

In this paper, we derive upper bounds for the heat kernel of the simple random walk on the infinite cluster of a supercritical long range percolation process. For any $d \geq 1$ and for any exponent $s \in (d, (d+2) \wedge 2d)$ giving the…

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using…

We give optimal bounds for the radial, space and time derivatives of arbitrary order of the heat kernel of the Laplace--Beltrami operator on Damek--Ricci spaces. In the case of symmetric spaces of rank one, these complete and actually…

We establish almost tight upper and lower approximation bounds for the Vertex Cover problem on dense k-partite hypergraphs.

We establish local asymptotic estimates of partial Bergman kernels on closed, $S^1$-symmetric K\"{a}hler manifolds. The main result concerns the scaling asymptotics of partial Bergman kernels at generic off-diagonal points in which they are…

We study the $2k$-th moment of central values of the family of Dirichlet $L$-functions to a fixed prime modulus. We establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $k$ in the range $0 \leq k \leq 1$.

We give matching upper and lower bounds for the Dirichlet heat kernel of a Schr\"odinger operator $\Delta+W$ in the domain above the graph of a bounded Lipschitz function, in the case when $W$ decays away from the boundary faster than…

We give lower bounds on the size and total size of clique partitions of a graph in terms of its spectral radius and minimum degree, and derive a spectral upper bound for the maximum number of edge-disjoint $t$-cliques. The extremal graphs…

We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…

On $\mathbb R^N$ equipped with a normalized root system $R$, a multiplicity function $k(\alpha) > 0$, and the associated measure $$ dw(\mathbf x)=\prod_{\alpha\in R}|\langle \mathbf x,\alpha\rangle|^{k(\alpha)}\, d\mathbf x, $$ let…

We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.

We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…