相关论文: Lebesgue constants on compact manifolds

We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order to do this, we also obtain log-scale lossless Strichartz and…

We prove the existence of approximate solutions in the (regular) Denjoy-Carleman sense for some systems of smooth complex vector fields. Such approximate solutions provide a well defined notion of Denjoy-Carleman wave front set of…

The purpose of this note is to discuss several results that have been obtained in the last decade in the context of sharp adjoint Fourier restriction/Strichartz inequalities. Rather than aiming at full generality, we focus on several…

We derive bilateral estimates for the constants appearing in the Fourier transform restricted theorems on the Euclidean sphere for the ordinary and especially radial functions belonging to the Lebesgue-Riesz spaces as well as belonging to…

We adapt the direct approach to the semiclassical Bergman kernel asymptotics, developed recently by A. Deleporte, J. Sj\"ostrand, and the first-named author for real analytic exponential weights, to the smooth case. Similar to that work,…

We prove the sharp regularizing estimates for the gain term of the Boltzmann collision operator including hard sphere, hard potential and Maxwell molecule models. Our new estimates characterize both regularization and convolution properties…

We investigate projection constants within classes of multivariate polynomials over finite-dimensional real Hilbert spaces. Specifically, we consider the projection constant for spaces of spherical harmonics and spaces of homogeneous…

The purpose of this paper is to establish that for any compact, connected C^{\infty} Riemannian manifold there exists a robust family of kernels of increasing smoothness that are well suited for interpolation. They generate Lagrange…

A well known conjecture states that constant functions are extremizers of the $L^2 \to L^6$ Tomas-Stein extension inequality for the circle. We prove that functions supported in a $\sqrt{6}/80$-neighbourhood of a pair of antipodal points on…

The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian manifolds,…

In 2004, J.C. Tong found bounds for the approximation quality of a regular continued fraction convergent of a rational number, expressed in bounds for both the previous and next approximation. We sharpen his results with a geometric method…

By application of the theory for second-order linear differential equations with two turning points developed in \cite{Olver1975}, uniform asymptotic approximations are obtained for the Lam\'{e} and Mathieu functions with a large real…

In the paper, we develop spectral theory to analyze the sharp asymptotic behavior of solutions to the Boltzmann equation around global Maxwellians in a three-dimensional infinite layer $\mathbb{R}^2\times (-1,1)$. The isothermal diffuse…

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…

We consider a compact complex manifold with smooth Levi convex boundary and a tame symplectic form. Consider a real two-sphere with elliptic and hyperbolic complex points generically embedded to the boundary of manifold. We prove a result…

Let $\{e_j\}$ be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold $(M,g)$. Let $H \subset M$ be a submanifold and let $\{\psi_k\}$ be an orthonormal basis of Laplace eigenfunctions of $H$ with the induced…

We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subspaces satisfying a highly generic and essentially optimal…

We investigate the uniform approximation provided by least squares polynomials on the unit Euclidean sphere $\mathbb{S}^q$ in $\mathbb{R}^{q+1}$, with $q\ge 2$. Like any other polynomial projection, the study concerns the growth, as the…

A concept of asymptotic symmetry is introduced which is based on a definition of symmetry as a reducibility property relative to a corresponding invariant ansatz. It is shown that the nonlocal Lorentz invariance of the free-particle…

We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2\pi$-periodic functions $\varphi$, such that $\|\varphi\|_2\le1$, with fixed generated kernels $\Psi_{\bar{\beta}}$,…