Related papers: Filtrations of dc-weak eigenforms
For 1<p< \infty, weight w \in A_p, and any L ^2 -bounded Calder\'on-Zygmund operator T, we show that there is a constant C(T,P) so that we prove the sharp norm dependence on T_#, the maximal truncations of T, in both weak and strong type…
We develop a new method that enables us to solve the open problem of characterizing discrete inequalities for kernel operators involving suprema. More precisely, we establish necessary and sufficient conditions under which there exists a…
Extending the approach of Iwaniec and Duke, we present strong uniform bounds for Fourier coefficients of half-integral weight cusp forms of level $N$. As an application, we consider a Waring-type problem with sums of mixed powers.
The slope of a p-adic overconvergent eigenform of weight k is the p-adic valuation of its U_p eigenvalue. We find the slope of all 2-adic finite slope overconvergent eigenforms of tame level 1 and weight 0. As a consequence we prove that…
We prove a general result on equality of the weak limits of the zero counting measure, $d\nu_n$, of orthogonal polynomials (defined by a measure $d\mu$) and $\frac{1}{n} K_n(x,x) d\mu(x)$. By combining this with Mate--Nevai and Totik upper…
In this article we investigate a special class of non-doubling metric measure spaces in order to describe the possible configurations of $P_{k,\rm s}^{\rm c}$, $P_{k,\rm s}$, $P_{k,\rm w}^{\rm c}$ and $P_{k,\rm w}$, the sets of all $p \in…
We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of…
We revisit a theorem of Ram Murty about the number of initial Fourier coefficients that two cuspidal eigenforms of different weights can have in common. We prove an explicit upper bound on this number, and give better conditional and…
The notion of local weak convergence, or Benjamini--Schramm convergence, was introduced by Benjamini and Schramm. The local weak limit of sparse Erd\H os--R\'enyi graphs is the Galton--Watson measure with Poisson offspring almost surely.…
We study congruences modulo powers of a prime $p$ between pairs of $p$-new modular Hecke eigenforms of level $\Gamma_0(p)$ and same weight $k$. Based on explicit computations, we conjecture that every such eigenform $f$ admits a twin to…
We are concerned with the nonexistence of sign-changing global weak solutions for a class of semilinear parabolic differential inequalities with convection terms in exterior domains. A weight function of the form $t^\alpha |x|^\sigma$ is…
We prove that for any weight $\phi$ defined on $[0,1]^n$ that satisfies a reverse Holder inequality with exponent p > 1 and constant $c\ge1$ upon all dyadic subcubes of $[0,1]^n$, it's non increasing rearrangement satisfies a reverse Holder…
Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…
We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue…
We study the problems of bounding the number weak and strong independent sets in $r$-uniform, $d$-regular, $n$-vertex linear hypergraphs with no cross-edges. In the case of weak independent sets, we provide an upper bound that is tight up…
In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a…
Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…
We give explicit upper bounds for the coefficients of arbitrary weight $k$, level 2 cusp forms, making Deligne's well-known $O(n^{\frac{k-1}{2}+\epsilon})$ bound precise. We also derive asymptotic formulas and explicit upper bounds for the…
We develop and analyze an ultraweak formulation of linear PDEs in nondivergence form where the coefficients satisfy the Cordes condition. Based on the ultraweak formulation we propose discontinuous Petrov--Galerkin (DPG) methods. We…