Related papers: Non-vanishing of Hilbert Poincar\'e series

We prove several theorems concerning the exceptional sets of Hilbert transform on the real line. In particular, it is proved that any null set is exceptional set for the Hibert transform of an indicator function. The paper also provides a…

In this paper, we characterize the sharp constant and maximizing functions for weighted Poincar\'e inequalities. These results lead to refinements of Hardy's inequality obtained by adding remainder terms involving \(L^p\) norms. We use…

We prove second and fourth order improved Poincar\'e type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as…

We study Euler-Poincare systems (i.e., the Lagrangian analogue of Lie-Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler-Poincare equations for a parameter dependent Lagrangian…

We prove here some dimension free Poincar\'e-type inequalities on Hamming cube for functions with different spectral properties and for fractional Laplacians. In this note the main attention is paid to estimates in $L^1$ norm on Hamming…

We prove that the field generated by the Fourier coefficients of weakly holomorphic Poincar\'e series of a given level $\Gamma_0(N)$ and weight $k\ge 2$ coincides with the field generated by the single-valued periods of a certain motive…

We address asymptotic formulae for the classical Poincar\'e-Perron problem of linear differential equations with almost constant coefficients in a half line $[t_0,+\infty)$ for high order equation $n\ge 5$ and some $t_0\in\mathbb{R}$. By…

We use dual graphs and generating sequences of valuations to compute the Poincare series of non-divisorial valuations on function fields of dimension two. The Poincare series are shown to reflect data from the dual graphs and hence carry…

In this paper, we show that incoherent Hilbert Eisenstein series for a real quadratic fields can be expressed as the Doi-Naganums lift of an incoherent Eisenstein series over $\mathbb{Q}$. As an application, we show when $N$ is odd and…

We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(\theta, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type…

In this paper, we prove the non-vanishing conjecture for cotangent bundles on isotrivial elliptic surfaces. Combined with the result by H\"{o}ring and Peternell, it completely solves the question for surfaces with Kodaira dimension at most…

We propose a systematic approach based on trajectories to prove a Poincar\'e inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of H\"ormander commutators, both in the local and in the…

A Poincar\'e-Einstein metric $g$ is called non-degenerate if there are no non-zero infinitesimal Einstein deformations of $g$, in Bianchi gauge, that lie in $L^2$. We prove that a 4-dimensional Poincar\'e-Einstein metric is non-degenerate…

The Fourier coefficients F(t) of a function f on a compact symmetric space U/K are given by integration of f against matrix coefficients of irreducible representations of U. The coefficients depend on a spectral parameter t, which…

In this short note, we provide a quantitative global Poincar\'e inequality for one forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on Ricci…

We give a number new examples analytically and numerically to confirm the Kohler conjecture. It turned out that for a rather large class of nonnegative functions the equality (A) hold.

We study manifolds satisfying a weighed Poincare inequality, which was first introduced by Li-Wang. We generalized one of their results by relaxing the Ricci curvature bound condition only being satisfied outside a compact set and…

This short and simple communication is motivated by recent papers by L. Colzani and A. Kochergin. We give a brief analysis of an example by Poincar\'{e} related to sums of the type $ \sum_{k=0}^{t-1} f(k{\alpha}+{x})$ where $f$ is a…

We generalize R. P. Stanley's celebrated theorem that the $h^\ast$-polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under containment of polytopes. We show that these results continue to…

A high dimensional dynamical system is often studied by experimentalists through the measurement of a relatively low number of different quantities, called an observation. Following this idea and in the continuity of Boshernitzan's work,…