Analytical continuation of two-dimensional wave fields

直角无对比可穿透楔体的衍射：谱函数的解析延拓

Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions

本文用双复变量Wiener-Hopf方法研究直角无对比可穿透楔体的衍射，证明谱函数可解析延拓至双复二维流形并揭示其奇点，提出加性穿越概念将物理问题转化为泛函问题。

多变量超几何函数的数值解析延拓

Numerical analytical continuation of multivariate hypergeometric functions

提出一个通用框架，通过构建Pfaffian系统和基于Frobenius方法的数值方案，实现多变量超几何函数的高精度数值评估与解析延拓。

通过解析延拓修正卡尔曼线性化中的发散

Fixing Divergence in Carleman Linearization via Analytical Continuation

研究针对卡尔曼线性化在求解非线性微分方程时出现的指数发散问题，通过解析延拓插入正则化函数进行校正，在逻辑斯谛方程等上验证了方法，并使用量子算法实现逻辑斯谛方程求解，给出复杂度和误差分析。

Uniqueness result for Almost Periodic Distributions depending on time and space and an application to the unique continuation for the wave equation

Let $Ω\subset \mathbb{R}^N$, $N=1,2,3$, be an open bounded and connected set with continuous piecewise $\mathrm{C}^{\infty}$ boundary. Here we deal with almost periodic distributions of the form $u(t,x)=\sum_{n=0}^{+\infty} c_n S_n(x) \mathrm{e}^{i λ_n t}$ where $(c_n)_{n\in \mathbb{N}}\subset \mathbb{C}$ belong to the space of slowing growing sequences $s^\prime$, and $(λ_n^2)_{n\in\mathbb{N}}\subset \mathbb{R}$ and $(S_n)_{n\in\mathbb{N}}\subset \mathrm{H}_0^{1}(Ω)$ are respectively the eigenvalues and eigenvectors of the Laplacian. Given $ω\subsetΩ$, we prove that there exists $T_{max}(Ω,ω)…

Unique continuation from infinity for linear waves

We prove various uniqueness results from null infinity, for linear waves on asymptotically flat space-times. Assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities, we derive that the solution must vanish in an open set in the interior. We find that the parts of infinity where we must impose a vanishing condition depend strongly on the background geometry. In particular, for backgrounds with positive mass (such as Schwarzschild or Kerr), the required assumptions are much weaker than the ones in the Minkowski space-time. The results are nearly …

Exact quantization and analytic continuation

In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrödinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the EQC to potentials with a regular singularity, describing spherical symmetric quantum mechanical systems in a given angular momentum sector. We show that the thermodynamic Bethe ansatz (TBA) equations that govern the quantum periods undergo nontrivial monodromies as the angular momentum is analytically continued between integer values in the complex …