薛定谔特征函数衰变和阿格蒙气泡的有效边界

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2024-08-04 DOI:10.1007/s11856-024-2641-x

Stefan Steinerberger

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引用次数: 0

摘要

我们研究-Δu + Vu = λu 在ℝn上的解。这些解在 "允许 "区域{x ∈ ℝn：V(x) ≤λ} ，并在 "禁止 "区域 {x∈ ℝn 内呈指数衰减：V(x) > λ} 。阿格蒙不等式是实现这一精确性的方法之一，它意味着以阿格蒙度量为基础的衰变估计。我们将阿格蒙度量与谐波度量的衰减联系起来，并证明了一个尖锐的阿格蒙点估计。

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Effective bounds for the decay of Schrödinger eigenfunctions and Agmon bubbles

We study solutions of −Δu + Vu = λu on ℝⁿ. Such solutions localize in the ‘allowed’ region {x ∈ ℝⁿ: V(x) ≤ λ} and decay exponentially in the ‘forbidden’ region {x ∈ ℝⁿ: V(x) > λ}. One way of making this precise is Agmon’s inequality implying decay estimates in terms of the Agmon metric. We prove a complementary decay estimate in terms of harmonic measure which can improve on Agmon’s estimate, connect the Agmon metric to decay of harmonic measure and prove a sharp pointwise Agmon estimate.

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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.