Related papers: Polynomial Fourier Decay For Patterson-Sullivan Me…
In a recent paper of Wolff the optimal decay of circular L^p means of compactly supported measures of finite energy was given for p>=2, with application to Falconer's distance problem. The question was then raised in that paper as to…
This work tackles the diffusive limit for the Vlasov-Poisson-Fokker-Planck model. We derive a priori estimates which hold without restriction on the phase-space dimension and propose a strong convergence result in a L2 space. Furthermore,…
We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these…
A deformation of the classical trigonometric BC(n) Sutherland system is derived via Hamiltonian reduction of the Heisenberg double of SU(2n). We apply a natural Poisson-Lie analogue of the Kazhdan-Kostant-Sternberg type reduction of the…
It is shown that, under a small perturbation of lump (soliton) for Davey--Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis…
Labourie and the author independently showed that a convex real projective structure on an oriented surface of genus at least 2 is equivalent to a conformal structure plus a holomorphic cubic differential U. We analyze the behavior of the…
We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use…
We investigate random Bernoulli convolutions, namely, probability measures given by the infinite convolution \[ \mu_\omega = \mathop{\circledast}_{k=1}^{\infty} \left( \frac{\delta_0 + \delta_{\lambda_1 \lambda_2 \ldots \lambda_{k-1}…
We prove moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that are sharp with respect to the scale parameter…
We develop a new transference method for completely bounded $L_p$-Fourier multipliers via proper cocycles arising from probability measure-preserving group actions. This method extends earlier results by Haagerup and Jolissaint, which were…
We consider the irreducibility of the regular representation of a noncompact semisimpe Lie group $G$ on the Hilbert space of the image of the Joint-Eigenspace Fourier transform on its corresponding symmetric space $G/K.$ The…
In this text we give a decomposition result on polynomial poly-vector fields generalizing a result on the decomposition of homogeneous Poisson structures. We discuss consequences of this decomposition result in particular for low dimensions…
We introduce a continuous analog of the Fourier ratio for compactly supported Borel measures. For a measure \(\mu\) on \(\mathbb{R}^d\) and \(f\in L^2(\mu)\), the Fourier ratio compares \(L^1\) and \(L^2\) norms of a regularized Fourier…
In this paper, we study the long time asymptotic behaviors for solutions to the Chern-Simons-Higgs equation with a pure power defocusing nonlinearity. We obtain quantitative inverse polynomial time decay for the potential energy for all…
We will extend the Fourier restriction inequality for quadratic hypersurfaces obtained by Strichartz. We will consider the case where the hypersurface is a graph of a certain real polynomial which is a sum of one-dimensional monomials. It…
We study the characteristic polynomial of random permutation matrices following some measures which are invariant by conjugation, including Ewens' measures which are one-parameter deformations of the uniform distribution on the permutation…
Let $\Gamma$ be a Gromov hyperbolic group, endowed with an arbitrary left-invariant hyperbolic metric, quasi-isometric to a word metric. The action of $\Gamma$ on its boundary $\partial\Gamma$ endowed with the Patterson-Sullivan measure…
In this paper we prove that decomposable forms, or homogeneous polynomials $F(x_1, \cdots, x_n)$ with integer coefficients which split completely into linear factors over $\mathbb{C}$, take on infinitely many square-free values subject to…
We prove that, given a torsion-free relatively hyperbolic group G with non-relatively-hyperbolic peripherals, isomorphic finite index subgroups of G have the same index. This applies for instance to fundamental groups of finite-volume…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…