Related papers: A Sharpened Inequality for Twisted Convolution
Let $f_1,...,f_d$ be an orthogonal basis for the space of cusp forms of even weight $2k$ on $\Gamma_0(N)$. Let $L(f_i,s)$ and $L(f_i,\chi,s)$ denote the $L$-function of $f_i$ and its twist by a Dirichlet character $\chi$, respectively. In…
We consider a mixed boundary value problem in a domain $\Omega$ contained in a half-ball $B_+$ and having a portion $\bar{T}$ of its boundary in common with the curved part of $\partial B_+$. The problem has to do with some sort of…
For a fixed $\theta\neq 0$, we define the twisted divisor function $$ \tau(n, \theta):=\sum_{d\mid n}d^{i\theta}\ .$$ In this article we consider the error term $\Delta(x)$ in the following asymptotic formula $$ \sum_{n\leq x}^*|\tau(n,…
Let $K$ be a number field of degree $d\geq 3$ and fix $s$ multiplicatively independent algebraic integers $\gamma_1, \dots, \gamma_s \in K^*$ that fulfil some technical requirements, which can be vastly simplified to $\mathbb{Q}$-linearly…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
The search of the optimal constant for a generalized Wirtinger inequality in an interval consists in minimizing the $p$-norm of the derivative among all functions whose $q$-norm is equal to~1 and whose $(r-1)$-power has zero average.…
In this paper we study Tikhonov regularization for the stable solution of an ill-posed non-linear operator equation. The operator we consider, which is related to an active contour model for image segmentation, is continuous, compact, but…
Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of…
We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply…
By methods based on elementary Linear Algebra we obtain sharp constants in cases of the Caffarelli-Kohn-Nirenberg inequality via quasi-conformal changes of variables. Some of our results were obtained earlier by Lam and Lu. Our proofs are…
An inequality of Brascamp-Lieb-Luttinger and of Rogers states that among subsets of Euclidean space $\mathbb{R}^d$ of specified Lebesgue measures, balls centered at the origin are maximizers of certain functionals defined by…
In this paper, we provide explicit formulas for the exact inverses of the symmetric tridiagonal near-Toeplitz matrices characterized by weak diagonal dominance in the Toeplitz part. Furthermore, these findings extend to scenarios where the…
We address the problem of finding worst-case nonparametric bounds for T-statistic by considering the extremal problem of maximising the mid-quantile (a special case of 'smoothed quantile' as discussed in \cite{St77} and \cite{W11}) $\tilde…
Given an ideal triangulation of a connected 3-manifold with non-empty boundary consisting of a disjoint union of tori, a point of the deformation variety is an assignment of complex numbers to the dihedral angles of the tetrahedra subject…
Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…
Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form $<,>$ on…
The goal of the article is to improve constants in the infimum convolution inequalities (IC for short) which were introduced by R. Lata{\l}a and J.O. Wojtaszczyk. We show that the exponential distribution satisfies IC with constant $2$ but…
The Neumann--Zagier matrices of an ideal triangulation are integer matrices with symplectic properties whose entries encode the number of tetrahedra that wind around each edge of the triangulation. They can be used as input data for the…
We find the optimal constant $C$ such that \begin{equation*} \|f_1*f_2*\dots*f_{k}\|_{\infty}\geq C\prod_{i=1}^{k}\|f_i\|_1 \end{equation*} for functions $f_i:\{0,1\}^d\to\mathbb{R}$. As applications, we derive bounds for Sidon sets on…
We study the evolution of a weakly convex surface $\Sigma_0$ in $\R^3$ with flat sides by the Harmonic Mean Curvature flow. We establish the short time existence as well as the optimal regularity of the surface and we show that the…