与Logvinenko-Sereda定理有关的一些结果

Scale-free unique continuation estimates and Logvinenko-Sereda Theorems on the torus

We study uncertainty principles for function classes on the torus. The classes are defined in terms of spectral subspaces of the energy or the momentum, respectively. In our main theorems, the support of the Fourier transform of the considered functions is allowed to be supported in a (finite number of) parallelepipeds. The estimates we obtain do not depend on the size of the torus and the position of the parallelepipeds, but only on their size and number, and the density and scale of the observability set. Our results are on the one hand closely related to unique continuation for linear combi…

紧流形上的 $L^p$-Logvinenko-Sereda 集与 $L^p$-Carleson 测度

$L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds

本文刻画了带或不带边界紧流形上所有$1<p<\infty$的$L^p$-Logvinenko-Sereda集与$L^p$-Carleson测度，进一步研究了无边界流形上特征函数的相应性质，并在标准球面上给出完整刻画与猜想，为相关开放问题提供了新进展。

紧流形上的Carleson测度与Logvinenko-Sereda集

Carleson Measures and Logvinenko-Sereda sets on compact manifolds

给定一个维数为$m\geq 2$的紧致黎曼流形$M$，研究了由$M$上Laplace-Beltrami算子的本征值小于$L\geq 1$的本征函数生成的$L^2(M)$的函数空间.在这些空间上，我们给出了Carleson测度和Logvinenko-Sereda集的特征。

Fourier-Bessel变换的Logvinenko-Sereda定理

The Logvinenko-Sereda Theorem for the Fourier-Bessel transform

本文的目的是建立$α>-1/2$阶Fourier-Bessel变换（或Hankel变换）$\ff_α$的Logvinenko-Sereda定理的一个类似定理。粗略地说，如果我们用$PW_α(b)$表示$[0,b]$中支持的具有Fourier-Bessel变换的$L^2$ -函数的Paley-Wiener空间，那么我们证明了限制映射$f\to f|_Ω$在$PW_α(b)$上本质可逆当且仅当$Ω$足够稠密.此外，我们给出了逆映射的范数的一个估计。作为一个副结果，我们证明了一个Bernstein型不等式的Fourier-Bessel变换。

关于空隙谱的Logvinenko-Sereda定理

A Logvinenko-Sereda theorem for lacunary spectra

本文研究了空隙谱函数的L2范数估计，证明了在E为实数集厚子集时，函数F的L2范数与F乘以特征函数χ_E的L2范数之间存在近似关系，扩展了Logvinenko-Sereda定理并回答了Kovrizhkin的问题。

Spectral estimates for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations

Some recent works have shown that the heat equation posed on the whole Euclidean space is null-controllable in any positive time if and only if the control subset is a thick set. This necessary and sufficient condition for null-controllability is linked to some uncertainty principles as the Logvinenko-Sereda theorem which give limitations on the simultaneous concentration of a function and its Fourier transform. In the present work, we prove new uncertainty principles for finite combinations of Hermite functions and establish an analogue of the Logvinenko-Sereda theorem with an explicit contro…