Journal of Functional Analysis最新文献

英文中文

Landau damping and survival threshold 朗道阻尼和生存阈值

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111357

Toan T. Nguyen

In this paper, we establish the large time asymptotic behavior of solutions to the linearized Vlasov-Poisson system near general spatially homogeneous equilibria

μ (\frac{1}{2} | v |^{2})

with connected support on the torus

T_{x}^{3} \times R_{v}^{3}

or on the whole space

R_{x}^{3} \times R_{v}^{3}

, including those that are non-monotone. The problem can be solved completely mode by mode for each spatial wave number, and their longtime dynamics is intimately tied to the “survival threshold” of wave numbers computed by

κ_{0}^{2} = 4 π \int_{0}^{ϒ} \frac{u^{2} μ (\frac{1}{2} u^{2})}{ϒ^{2} - u^{2}} d u

where ϒ is the maximal speed of particle velocities. It is shown that purely oscillatory electric fields exist and obey a Klein-Gordon's type dispersion relation for wave numbers below and up to the threshold, thus rigorously confirming the existence of Langmuir's oscillatory waves for a non-trivial range of spatial frequencies in this linearized setting. At the threshold, the phase velocity of these oscillatory waves enters the range of admissible particle velocities, namely there are particles that move at the same propagation speed of the waves. It is this exact resonant interaction between particles and the oscillatory fields that causes the waves to be damped, classically known as Landau damping. Landau's law of decay is explicitly computed and is sensitive to the decaying rate of the background equilibria. The faster it decays at the maximal velocity, the weaker Landau damping is. Beyond the threshold, the electric fields are a perturbation of those generated by the free transport dynamics and thus decay rapidly fast due to the phase mixing mechanism.

本文在环面Tx3×Rv3或整个空间Rx3×Rv3上，建立了具有连通支撑的一般空间齐次平衡点μ(12|v|2)附近线性化Vlasov-Poisson系统解的大时渐近性，包括非单调的解。对于每个空间波数，这个问题可以通过一个模式一个模式地完全解决，它们的长期动态与由κ02=4π∫0ϒu2μ(12u2)ϒ2−u2du计算的波数的“生存阈值”密切相关，其中y是粒子速度的最大速度。结果表明，在阈值以下和阈值以上的波数存在纯振荡电场，且服从Klein-Gordon型色散关系，从而严格证实了在线性化条件下，在非平凡的空间频率范围内存在Langmuir振荡波。在阈值处，这些振荡波的相速度进入允许的粒子速度范围，即存在与波的传播速度相同的粒子。正是这种粒子与振荡场之间的共振相互作用导致了波的衰减，即经典的朗道阻尼。朗道衰减定律是明确计算的，并且对背景平衡态的衰减速率敏感。在最大速度下衰减越快，朗道阻尼越弱。超过阈值，电场是由自由输运动力学产生的扰动，因此由于相位混合机制而迅速衰减。

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引用次数: 0

Fractional boundary Hardy inequality for the critical cases 临界情况下的分数边界Hardy不等式

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111351

Adimurthi, Prosenjit Roy, Vivek Sahu

We establish generalized fractional boundary Hardy-type inequality, in the spirit of Caffarelli-Kohn-Nirenberg inequality for different values of s and p on various domains in

R^{d}, d \geq 1

. In particular, for Lipschitz bounded domains any values of s and p are admissible, settling all the cases in subcritical, supercritical and critical regime. In this paper we have solved the open problems posed by Dyda for the critical case

s p = 1

. Moreover we have proved the embeddings of

W_{0}^{s, p} (Ω)

in subcritical, critical and supercritical uniformly without using Dyda's decomposition. Additionally, we extend our results to include a weighted fractional boundary Hardy-type inequality for the critical case.

根据Caffarelli-Kohn-Nirenberg不等式的精神，在Rd，d≥1的不同定域上，对s和p的不同值，建立了广义分数阶边界hardy型不等式。特别地，对于Lipschitz有界区域，s和p的任何值都是允许的，解决了在亚临界、超临界和临界区域的所有情况。在sp=1的临界情况下，我们解决了由Dyda提出的开放问题。此外，我们还在不使用Dyda分解的情况下，均匀地证明了W0s、p（Ω）在亚临界、临界和超临界中的嵌入。此外，我们扩展了我们的结果，以包含临界情况下的加权分数边界hardy型不等式。

引用次数: 0

Lower semicontinuity and existence results for anisotropic TV functionals with signed measure data 带符号测量数据的各向异性TV泛函的下半连续性和存在性结果

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111350

Eleonora Ficola, Thomas Schmidt

We study the minimization of anisotropic total variation functionals with additional measure terms among functions of bounded variation subject to a Dirichlet boundary condition. More specifically, we identify and characterize certain isoperimetric conditions, which prove to be sharp assumptions on the signed measure data in connection with semicontinuity, existence, and relaxation results. Furthermore, we present a variety of examples which elucidate our assumptions and results.

研究了具有狄利克雷边界条件的有界变分函数中具有附加测度项的各向异性全变分泛函的最小化问题。更具体地说，我们识别和表征了某些等周条件，这些条件证明了与半连续性、存在性和松弛结果有关的有符号测量数据的尖锐假设。此外，我们提出了各种例子来阐明我们的假设和结果。

引用次数: 0

Transfer between theta lifts of trivial representations 平凡表示的提升之间的转换

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111353

Ning Li , Chuijia Wang

The notion of transfer is a way to relate representations of different real forms of a complex semisimple Lie group. It has been investigated that there is a close connection between local theta correspondence and the procedure of transfer by the pioneer work of Wallach–Zhu. In this paper, we focus on the transfer of irreducible unitary constituents of the degenerate principal series representations of

Sp (2 n, R)

. In particular, we show that every irreducible unitary constituent of the big theta lift from

O (p, q)

Sp (2 n, R)

of the trivial character can be realized as a transfer of the small theta lift from the compact orthogonal group

O (0, p + q)

Sp (2 n, R)

of the trivial character via the study of K-types. This partially confirms a conjecture of Wallach–Zhu on the internal structure of theta lifts in the non-stable range case.

迁移的概念是将复半单李群的不同实形式的表示联系起来的一种方法。瓦拉赫-朱的开创性工作研究了局部θ对应与迁移过程之间的密切联系。本文研究Sp（2n，R）的退化主级数表示的不可约酉元的转移。特别地，我们证明了从平凡特征的O（p,q）到Sp（2n，R）的大升力的每一个不可约的酉成分都可以通过研究k型来实现从平凡特征的紧正交群O（0,p+q）到Sp（2n，R）的小升力的转移。这部分证实了Wallach-Zhu在非稳定范围情况下关于theta升降机内部结构的猜想。

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引用次数: 0

Non-strict singularity of optimal Sobolev embeddings 最优Sobolev嵌入的非严格奇异性

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-12 DOI: 10.1016/j.jfa.2026.111344

Jan Lang , Zdeněk Mihula

We investigate the operator-theoretic property of strict singularity for optimal Sobolev embeddings within the general framework of rearrangement-invariant function spaces (r.i. spaces).

More specifically, we focus on studying the “quality” of non-compactness for optimal Sobolev embeddings

V_{0}^{m} X (Ω) \to Y_{X} (Ω)

, where X is a given r.i. space and

Y_{X}

is the corresponding optimal target r.i. space (i.e., the smallest among all r.i. spaces).

For the class of sub-limiting norms (i.e., the norms whose fundamental function satisfies

φ_{Y_{X}} (t) \approx t^{- m / n} φ_{X} (t)

t \to 0^{+}

), we construct suitable spike-function sequences that establish a general framework for proving non-strict singularity of optimal (and thus non-compact) sublimiting Sobolev embeddings.

As an application, we show that optimal sublimiting Sobolev embeddings are not strictly singular in a rather large subclass of r.i. spaces, namely weighted Lambda spaces

X = Λ_{w}^{q}

q \in [1, \infty)

. Except for the endpoint case

X = L^{n / m, 1}

, our spike-function construction enables us to construct a subspace of

V_{0}^{m} X

that is isomorphic to

ℓ_{q}

, which we then leverage to prove the non-strict singularity of the corresponding optimal Sobolev embedding.

在重排不变函数空间的一般框架下，研究了最优Sobolev嵌入的严格奇异性的算子理论性质。更具体地说，我们专注于研究最优Sobolev嵌入V0mX（Ω）→YX（Ω）的非紧性的“质量”，其中X是给定的r.i空间，而YX是相应的最优目标r.i空间（即所有r.i空间中最小的）。对于一类次极限范数(即基本函数满足φYX（t)≈t−m/nφX(t) = t→0+的范数），我们构造了合适的峰值函数序列，建立了证明最优次极限Sobolev嵌入的非严格奇异性的一般框架。作为一个应用，我们证明了最优次限Sobolev嵌入在一个相当大的r.i.空间子类，即加权Lambda空间X=Λwq, q∈[1，∞]中不是严格奇异的。除了端点情况X=Ln/m，1外，我们的峰值函数构造使我们能够构造V0mX的子空间，该子空间与lq同构，然后我们利用它来证明相应的最优Sobolev嵌入的非严格奇异性。

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引用次数: 0

Asymptotic pseudodifferential calculus and the rescaled bundle 渐近伪微分学与重标束

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-12 DOI: 10.1016/j.jfa.2026.111354

Xiaoman Chen , Zelin Yi

By following a groupoid approach to pseudodifferential calculus developed by Van Erp and Yuncken, we study the parallel theory on the rescaled bundle and show that the rescaled bundle gives a geometric characterization of the asymptotic pseudodifferential calculus on spinor bundles by Block and Fox.

利用Van Erp和Yuncken提出的伪微分学的群似方法，研究了重标束上的并行理论，并证明了重标束给出了Block和Fox在旋量束上的渐近伪微分学的几何表征。

引用次数: 0

Curvature pinching estimate under the Laplacian G2 flow 拉普拉斯G2流下的曲率捏缩估计

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-01 Epub Date: 2025-09-17 DOI: 10.1016/j.jfa.2025.111199

Chuanhuan Li , Yi Li

In this paper, we derive a pinching estimate for the traceless Ricci curvature in terms of scalar curvature and the

C^{1}

norm of the Weyl tensor under the Laplacian

G_{2}

flow for closed

G_{2}

structures. Then we apply this estimate to study the long time existence of the Laplacian

G_{2}

flow and prove that the

C^{1}

norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.

本文用标量曲率和闭G2结构下Laplacian G2流下Weyl张量的C1范数，导出了无迹Ricci曲率的捏缩估计。然后应用这一估计研究了拉普拉斯G2流的长时间存在性，证明了Weyl张量的C1范数在有界标量曲率下必须至少以一定的速率爆炸。

引用次数: 0

Optimal decay of eigenvector overlap for non-Hermitian random matrices 非厄米随机矩阵特征向量重叠的最优衰减

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-01 Epub Date: 2025-09-01 DOI: 10.1016/j.jfa.2025.111180

Giorgio Cipolloni , László Erdős , Yuanyuan Xu

We consider the standard overlap

O_{i j} : = 〈 r_{j}, r_{i} 〉 〈 l_{j}, l_{i} 〉

of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge.

我们考虑一个大随机矩阵X的任意双正交的左右特征向量族的标准重叠Oij:= < rj,ri > < lj,li >，我们证明了它衰减为对应特征值之间距离的倒数次幂。这将复高斯系综的类似结果从Bourgade和Dubach[15]，以及Benaych-Georges和Zeitouni[13]推广到两种对称类中的任何i.i.d矩阵系综。作为一种主要工具，我们证明了X在光谱中均匀地具有最佳衰减率和最优依赖于谱边附近密度的双解局域律。

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引用次数: 0

Corrigendum to: “Quantization and the resolvent algebra” [J. Funct. Anal. 277 (8) (2019) 2815–2838] “量化与求解代数”的勘误[J]。功能。肛门。277 (8)(2019)2815-2838]

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-01 Epub Date: 2025-09-03 DOI: 10.1016/j.jfa.2025.111184

Teun D.H. van Nuland, Lorenzo Pettinari

In [3] it is claimed incorrectly that the Berezin quantization map maps surjectively to the resolvent algebra.¹ We show here that it does not. Similarly, the Berezin map defined on

C_{0} (R^{2 n})

does not reach all compact operators, contrary to what is claimed in [2, II.(2.73)].² We moreover fill a gap in the proof of injectivity of the Berezin quantization map on

C_{R} (X)

of [3].

在[3]中，错误地认为Berezin量化映射主观地映射到可解代数我们在这里证明它不是。同样，定义在C0（R2n）上的Berezin映射不能到达所有紧算子，这与[2，II.(2.73)].2中所述的相反此外，我们还填补了[3]的Berezin量化映射在CR(X)上注入性证明的空白。

引用次数: 0

Spectrum of invertible weighted composition operators on the unit disk 单位圆盘上可逆加权复合算子的谱

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-01 Epub Date: 2025-08-29 DOI: 10.1016/j.jfa.2025.111186

Jesús Oliva-Maza

The spectrum of invertible weighted composition operators

u C_{φ}

acting on classical Banach spaces of holomorphic functions in the unit disk

D

has been studied intensively over the years. Complete descriptions of that spectrum have been given in the elliptic or parabolic cases, that is, for φ either elliptic or parabolic, but only partial results have been obtained in the remaining case, that is, for hyperbolic φ. In this paper, we give the spectrum and the essential spectrum of

u C_{φ}

for hyperbolic φ. Our results answer in the positive several conjectures posed by different authors.

In order to deal with the above questions, we present new techniques which involve the embedding of the weight u into a cocycle

{(u_{t})}_{t \in R}

associated to an hyperbolic flow

{(φ_{t})}_{t \in R}

. We also provide information about the range spaces and null spaces of

λ - u C_{φ}

for λ lying in the interior of

σ (u C_{φ})

近年来，人们对单位盘D上全纯函数的经典巴拿赫空间上的可逆加权复合算子uCφ的谱进行了深入的研究。在椭圆型或抛物线型情况下，即对于椭圆型或抛物线型φ，已经给出了该谱的完整描述，但在其余情况下，即对于双曲型φ，只得到了部分结果。本文给出了双曲型φ的谱和本质谱。我们的结果肯定地回答了不同作者提出的几个猜想。为了解决上述问题，我们提出了一种新技术，将权重u嵌入到与双曲流（φt）t∈R相关的循环（ut）t∈R中。对于λ位于σ(uCφ)的内部，我们也给出了λ−uCφ的值域空间和零空间的信息。

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引用次数: 0

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