Journal of Functional Analysis最新文献

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The character correspondence in the stable range over a p-adic field 在p进域的稳定范围内的字符对应

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-02-09 DOI: 10.1016/j.jfa.2026.111392

Hung Yean Loke , Tomasz Przebinda

Given a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the group with the larger or equal rank. If the pair is in the stable range and if the representation is unitary, then the resulting distribution is the character of the representation obtained via Howe's correspondence. This construction was transferred to the p-adic case and a conjecture was formulated.

In this note we verify a weaker version of this conjecture for dual pairs in the stable range over a p-adic field.

给定一个实不可约对偶对，存在一个积分核算子，它将秩较小或相等的群的不可约容许表示的分布特征映射到秩较大或相等的群上的不变特征分布。如果对在稳定范围内，并且表示是酉的，则得到的分布是通过Howe对应得到的表示的特征。将这种构造转化为p进情形，并给出了一个猜想。在本文中，我们对p进域上稳定范围内的对偶对验证了这个猜想的一个弱版本。

引用次数: 0

A characterization of generalized functions of bounded deformation 一类有界变形广义函数的刻画

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-02-06 DOI: 10.1016/j.jfa.2026.111391

Antonin Chambolle , Vito Crismale

We show that Dal Maso's GBD space, introduced for tackling crack growth in linearized elasticity, can be defined by simple conditions in a finite number of directions of slicing.

我们证明了Dal Maso的GBD空间，用于处理线性化弹性中的裂纹扩展，可以用有限个切片方向上的简单条件来定义。

引用次数: 0

Thin spectra for periodic and ergodic word models 周期和遍历词模型的薄谱

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-02-05 DOI: 10.1016/j.jfa.2026.111385

Jake Fillman , Michala N. Gradner , Hannah J. Hendricks

We establish a new and simple criterion that suffices to generate many spectral gaps for periodic word models. This leads to new examples of ergodic Schrödinger operators with Cantor spectra having zero Hausdorff dimension that simultaneously may have arbitrarily small supremum norm together with arbitrarily long runs on which the potential vanishes.

我们建立了一个新的和简单的准则，足以产生许多谱间隙周期词模型。这导致了新的遍历Schrödinger算子的例子，其康托尔谱具有零豪斯多夫维数，同时可能具有任意小的最高范数和任意长的运行，在此运行上势能消失。

引用次数: 0

A simple proof of reverse Sobolev inequalities on the sphere and Sobolev trace inequalities on the unit ball 球面上的索博列夫反不等式和单位球上的索博列夫迹不等式的简单证明

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-26 DOI: 10.1016/j.jfa.2026.111380

Runmin Gong , Qiaohua Yang , Shihong Zhang

Frank et al. (2022) [38] stated that there is no relation between the reversed Hardy-Littlewood-Sobolev (HLS) inequalities and reverse Sobolev inequalities. However, we demonstrate that reverse Sobolev inequalities of order

γ \in (\frac{n}{2}, \frac{n}{2} + 1)

on the n-sphere can be readily derived from the reversed HLS inequalities. For the case

γ \in (\frac{n}{2} + 1, \frac{n}{2} + 2)

, we present a simple proof of reverse Sobolev inequalities by using the center of mass condition introduced by Hang. In addition, applying this approach, we establish the quantitative stability of reverse Sobolev inequalities of order

γ \in (\frac{n}{2} + 1, \frac{n}{2} + 2)

with explicit lower bounds. Finally, by using conformally covariant boundary operators and reverse Sobolev inequalities, we derive Sobolev trace inequalities on the unit ball.

Frank et al.(2022)[38]指出，反向Hardy-Littlewood-Sobolev （HLS）不等式与反向Sobolev不等式之间没有关系。然而，我们证明了n球上γ∈(n2,n2+1)阶的反Sobolev不等式可以很容易地由反HLS不等式导出。对于γ∈(n2+1,n2+2)的情况，利用Hang引入的质心条件，给出了逆Sobolev不等式的一个简单证明。此外，利用该方法，我们建立了γ∈(n2+1,n2+2)阶逆Sobolev不等式具有明确下界的定量稳定性。最后，利用共形协变边界算子和逆Sobolev不等式，导出了单位球上的Sobolev迹不等式。

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引用次数: 0

Transition threshold of Couette flow for 2D Boussinesq equations 二维Boussinesq方程的Couette流的过渡阈值

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-23 DOI: 10.1016/j.jfa.2026.111383

Xiaoxia Ren , Dongyi Wei

In this paper, we prove the stability threshold of

\frac{1}{3}

for 2D Boussinesq equations around the Couette flow in

T \times R

with Richardson number

γ^{2} > \frac{1}{4}

and different viscosity ν and thermal diffusivity μ. More precisely, if

{‖ v_{i n} - (y, 0) ‖}_{H^{s + 1 / 2}} + {‖ ρ_{i n} + γ^{2} y - 1 ‖}_{H^{s + 1 / 2}} \leq c {(\min {ν, μ})}^{1 / 3}

\frac{ν + μ}{2 γ \sqrt{ν μ}} < 2 - ε

s > \frac{3}{2}

, then the asymptotic stability holds. This stability threshold is consistent with the optimal stability threshold for the 2D Navier-Stokes equations in Sobolev space. And in the sense of inviscid damping effect, the regularity assumption of the initial data should be sharp.

本文证明了含有理查德森数γ2>；14、不同粘度ν和热扩散系数μ的T×R中Couette流动的二维Boussinesq方程的稳定性阈值为13。更准确地说,如果为vin−(y, 0)为h + 1/2 +为ρy +γ2−1为h + 1/2≤c(最低⁡{ν,μ})1/3,ν+μ2γνμ& lt; 2−ε,s> 32,渐近稳定。该稳定性阈值与Sobolev空间中二维Navier-Stokes方程的最优稳定性阈值一致。在无粘阻尼效应的意义上，初始数据的正则性假设应该是尖锐的。

引用次数: 0

On a class of nonlinear BGK-type kinetic equations with density dependent collision rates 一类具有密度相关碰撞率的非线性bgk型动力学方程

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-23 DOI: 10.1016/j.jfa.2026.111376

Josephine Evans , Daniel Morris , Havva Yoldaş

We consider a class of nonlinear, spatially inhomogeneous kinetic equations of BGK-type with density dependent collision rates. These equations share the same superlinearity as the Boltzmann equation, and fall into the class of run and tumble equations appearing in mathematical biology. We prove that the Cauchy problem is well-posed, and the solutions propagate Maxwellian bounds over time. Moreover, we show that the solutions approach to equilibrium with an exponential rate, known as a hypocoercivity result. Lastly, we derive a class of nonlinear diffusion equations as the hydrodynamic limit of the kinetic equations in the diffusive scaling, employing both hypocoercivity and relative entropy methods. The limit equations cover a wide range of nonlinear diffusion equations including both the porous medium and the fast diffusion equations.

考虑一类具有密度相关碰撞率的非线性空间非齐次bgk型动力学方程。这些方程与玻尔兹曼方程具有相同的超线性，属于数学生物学中出现的奔跑和翻滚方程。我们证明了柯西问题是适定的，并且解随时间传播麦克斯韦界。此外，我们证明了解以指数速率接近平衡，称为准矫顽力结果。最后，利用准矫顽力法和相对熵法，导出了一类非线性扩散方程作为扩散标度中动力学方程的水动力极限。极限方程涵盖了广泛的非线性扩散方程，既包括多孔介质，也包括快速扩散方程。

引用次数: 0

Large deviation principles for stochastic nonlinear Schrödinger equations driven by Lévy noise l<s:1>杂讯驱动随机非线性Schrödinger方程的大偏差原理

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-23 DOI: 10.1016/j.jfa.2026.111377

Jiahui Zhu , Wei Liu , Jianliang Zhai

In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic nonlinear Schrödinger equation, with either focusing or defocusing nonlinearity, driven by nonlinear multiplicative Lévy noise in the Marcus canonical form. This task is challenging in the current setting due to the presence of the power-type nonlinear term, the lack of regularization effect of the Schrödinger operator and the absence of compactness of embeddings. To overcome these difficulties, we employ a regularization procedure based on Yosida approximations and implement techniques such as time discretization, cut-off arguments, and relative entropy estimates of sequences of probability measures. Our innovative approach circumvents the need for compactness conditions, distinguishing our work from previous studies.

本文建立了具有聚焦或散焦非线性的随机非线性Schrödinger方程的Freidlin-Wentzell型大偏差原理，该方程由Marcus标准形式的非线性乘性lsamvy噪声驱动。由于幂型非线性项的存在、Schrödinger算子的正则化效果的缺乏以及嵌入的紧性的缺乏，这项任务在当前的设置中是具有挑战性的。为了克服这些困难，我们采用了基于Yosida近似的正则化过程，并实现了时间离散化、截止参数和概率测量序列的相对熵估计等技术。我们的创新方法绕过了对紧凑性条件的需求，将我们的工作与以前的研究区分开来。

引用次数: 0

Quantum dynamical bounds for long-range operators with skew-shift potentials 具有斜移势的远程算符的量子动力学界

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-23 DOI: 10.1016/j.jfa.2026.111378

Wencai Liu , Matthew Powell , Xueyin Wang

We employ Weyl's method and Vinogradov's method to analyze skew-shift dynamics on semi-algebraic sets. Consequently, we improve the quantum dynamical upper bounds of Jitomirskaya-Powell, Liu, and Shamis-Sodin for long-range operators with skew-shift potentials.

采用Weyl方法和Vinogradov方法分析了半代数集上的偏移动力学。因此，我们改进了Jitomirskaya-Powell， Liu和Shamis-Sodin对于具有斜移势的远程算子的量子动力学上界。

引用次数: 0

Holomorphic induction beyond the norm-continuous setting, with applications to positive energy representations 超越范数连续设定的全纯归纳，并应用于正能量表示

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-23 DOI: 10.1016/j.jfa.2026.111382

Milan Niestijl

We extend the theory of holomorphic induction of unitary representations of a possibly infinite-dimensional Lie group G beyond the setting where the representation being induced is required to be norm-continuous. We allow the group G to be a connected BCH (Baker–Campbell–Hausdorff) Fréchet–Lie group. Given a smooth

R

-action α on G, we proceed to show that the corresponding class of so-called positive energy representations is intimately related with holomorphic induction. Assuming that G is regular, we in particular show that if ρ is a unitary ground state representation of

G ⋊_{α} R

for which the energy-zero subspace

H_{ρ} (0)

admits a dense set of G-analytic vectors, then

{ρ |}_{G}

is holomorphically induced from the representation of the connected subgroup

H : = {(G^{α})}_{0}

of α-fixed points on

H_{ρ} (0)

. As a consequence, we obtain an isomorphism

B {(H_{ρ})}^{G} ≅ B {(H_{ρ} (0))}^{H}

between the corresponding commutants. We also find that two such ground state representations are unitarily equivalent if and only if their energy-zero subspaces are unitarily equivalent as H-representations. These results were previously only available under the assumption of norm-continuity of the H-representation on

H_{ρ} (0)

我们将可能无限维李群G的酉表示的全纯归纳理论推广到要求所归纳的表示是范数连续的集合之外。我们允许G群是一个连通的BCH (Baker-Campbell-Hausdorff) fr chet - lie群。给定G上的光滑r作用α，我们进一步证明了相应的一类所谓的正能量表示与全纯归纳密切相关。假设G是正则的，我们特别证明了如果ρ是G αR的酉基态表示，其能量零子空间Hρ(0)允许G解析向量的密集集合，那么ρ|G是由Hρ(0)上α-不动点的连通子群H:=(Gα)0的表示全纯导出的。因此，我们得到了相应交换子之间的同构B(Hρ)G = B(Hρ(0))H。我们还发现两个这样的基态表示当且仅当它们的能量零子空间与h表示一致时是等价的。这些结果以前只能在Hρ(0)上的h表示的范数连续性假设下才能得到。

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引用次数: 0

A splitting theorem for manifolds with nonnegative spectral Ricci curvature and mean convex boundary 具有非负谱Ricci曲率和平均凸边界流形的分裂定理

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-23 DOI: 10.1016/j.jfa.2026.111381

Han Hong , Gaoming Wang

We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension

n \geq 2

has

λ_{1} (- α Δ + Ric) \geq 0

for some

α < \frac{4}{n - 1}

and mean convex boundary, then it is either isometric to

Σ \times R_{\geq 0}

for a closed manifold Σ with nonnegative Ricci curvature or it has no interior ends.

我们证明了具有（可能是非紧的）边界的光滑非紧流形的分裂定理。我们证明了如果一个维数n≥2的非紧流形对于某些α<；4n−1和平均凸边界具有λ1(−αΔ+Ric)≥0，那么对于一个具有非负Ricci曲率的闭流形Σ，它要么与Σ×R≥0是等距的，要么没有内端。

引用次数: 0

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