Zobrazeno 1 - 10
of 505
pro vyhledávání: '"35S30"'
Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in $L^2(\mathbb{R}^d)$ and its Fourier transform cannot both decay arbitrarily fast at infinity. In this paper, we extend this principle to the propagat
Externí odkaz:
http://arxiv.org/abs/2410.13818
Autor:
Prouff, Antoine
We prove a general version of Egorov's theorem for evolution propagators in the Euclidean space, in the Weyl--H\"ormander framework of metrics on the phase space. Mild assumptions on the Hamiltonian allow for a wide range of applications that we desc
Externí odkaz:
http://arxiv.org/abs/2412.04320
Autor:
Jia, Qiuye, Zhang, Junyong
We study the pointwise decay estimates for the Schr\"odinger and wave equations on a product cone $(X,g)$, where the metric $g=dr^2+r^2 h$ and $X=C(Y)=(0,\infty)\times Y$ is a product cone over the closed Riemannian manifold $(Y,h)$ with metric $h$.
Externí odkaz:
http://arxiv.org/abs/2411.16029
Autor:
Blair, Matthew D., Park, Chamsol
We consider restriction analogues on hypersurfaces of the uniform Sobolev inequalities in Kenig, Ruiz, and Sogge and the resolvent estimates in Dos Santos Ferreira, Kenig, and Salo.
Externí odkaz:
http://arxiv.org/abs/2411.04792
Autor:
Cobb, Dimitri, Koch, Herbert
In this article, we will study unbounded solutions of the 2D incompressible Euler equations. One of the motivating factors for this is that the usual functional framework for the Euler equations (e.g. based on finite energy conditions, such as $L^2$)
Externí odkaz:
http://arxiv.org/abs/2410.05054
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial differential
Externí odkaz:
http://arxiv.org/abs/2409.11998
Autor:
Thakkar, Chandni
In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray transform is rest
Externí odkaz:
http://arxiv.org/abs/2409.09341
Autor:
Sampedro, Juan Carlos
In this paper we use abstract bifurcation theory for Fredholm operators of index zero to deal with periodic even solutions of the one-dimensional equation $\mathcal{L}u=\lambda u+|u|^{p}$, where $\mathcal{L}$ is a nonlocal pseudodifferential operator
Externí odkaz:
http://arxiv.org/abs/2409.04253
Autor:
Zhu, Xiangrong, Li, Wenjuan
Let $n\geq 1,0<\rho<1, \max\{\rho,1-\rho\}\leq \delta\leq 1$ and $$m_1=\rho-n+(n-1)\min\{\frac 12,\rho\}+\frac {1-\delta}{2}.$$ If the amplitude $a$ belongs to the H\"{o}rmander class $S^{m_1}_{\rho,\delta}$ and $\phi\in \Phi^{2}$ satisfies the stron
Externí odkaz:
http://arxiv.org/abs/2408.15280
The purpose of this study is twofold. First, we revisit a shape optimization reformulation of a prototypical shape inverse problem and briefly propose a simple yet efficient numerical approach for solving the minimization problem. Second, we examine
Externí odkaz:
http://arxiv.org/abs/2407.03083