Journal of Functional Analysis最新文献

英文中文

Classification of equivariantly O2-stable amenable actions on nuclear C⁎-algebras 核 C⁎-代数上等变 O2 稳定可配作用的分类

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-16 DOI: 10.1016/j.jfa.2024.110683

Matteo Pagliero, Gábor Szabó

Given a second-countable, locally compact group G, we consider amenable G-actions on separable, stable, nuclear

C^{⁎}

-algebras that are isometrically shift-absorbing and tensorially absorb the trivial action on the Cuntz algebra

O_{2}

. We show that such actions are classified up to cocycle conjugacy by the induced G-action on the primitive ideal space. In the special case when G is exact, we prove a unital version of our classification theorem. For compact groups, we obtain a classification up to conjugacy.

给定一个二次可数局部紧密群 G，我们考虑可分离、稳定、核 C⁎-原子团上的可处理 G 作用，这些作用等效地吸收移位，并张量地吸收 Cuntz 代数 O2 上的琐细作用。我们的研究表明，这种作用是由原始理想空间上的诱导 G 作用分类到共轭循环的。在 G 是精确的特殊情况下，我们证明了我们的分类定理的单元版本。对于紧凑群，我们得到了直至共轭的分类。

引用次数: 0

High moments of the SHE in the clustering regimes 聚类机制中的 SHE 高矩阵

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-16 DOI: 10.1016/j.jfa.2024.110675

Li-Cheng Tsai

We analyze the high moments of the Stochastic Heat Equation (SHE) via a transformation to the attractive Brownian Particles (BPs), which are Brownian motions interacting via pairwise attractive drift. In those scaling regimes where the particles tend to cluster, we prove a Large Deviation Principle (LDP) for the empirical measure of the attractive BPs. Under the delta(-like) initial condition, we characterize the unique minimizer of the rate function and relate the minimizer to the spacetime limit shapes of the Kardar–Parisi–Zhang (KPZ) equation in the upper tails. The results of this paper are used in the companion paper [75] to prove an n-point, upper-tail LDP for the KPZ equation and to characterize the corresponding spacetime limit shape.

我们分析了随机热方程（SHE）的高矩，将其转换为有吸引力的布朗粒子（BPs），即通过成对吸引力漂移相互作用的布朗运动。在粒子趋于聚集的缩放状态下，我们证明了吸引力布朗粒子经验度量的大偏差原理（LDP）。在 delta（-like）初始条件下，我们描述了速率函数的唯一最小值，并将该最小值与 Kardar-Parisi-Zhang (KPZ) 方程在上尾部的时空极限形状联系起来。本文的结果被用在同行论文[75]中，证明了 KPZ 方程的 n 点上尾 LDP，并描述了相应的时空极限形状。

引用次数: 0

Singular extension of critical Sobolev mappings under an exponential weak-type estimate 指数弱型估计下临界索波列夫映射的奇异扩展

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-16 DOI: 10.1016/j.jfa.2024.110681

Bohdan Bulanyi , Jean Van Schaftingen

Given

m \in N ∖ {0}

and a compact Riemannian manifold

N

, we construct for every map u in the critical Sobolev space

W^{m / (m + 1), m + 1} (S^{m}, N)

, a map

U : B_{1}^{m + 1} \to N

whose trace is u and which satisfies an exponential weak-type Sobolev estimate. The result and its proof carry on to the extension to a half-space of maps on its boundary hyperplane and to the extension to the hyperbolic space of maps on its boundary sphere at infinity.

给定 m∈N∖{0} 和一个紧凑的黎曼流形 N，我们为临界索波列夫空间 Wm/(m+1),m+1(Sm,N)中的每一个映射 u 构建一个映射 U:B1m+1→N，其迹线为 u 并且满足指数弱型索波列夫估计。该结果及其证明可延伸至边界超平面上映射的半空间，以及边界球面上映射的无穷远处的双曲空间。

引用次数: 0

Higher index theory for spaces with an FCE-by-FCE structure 具有逐FCE结构的空间的高指数理论

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-16 DOI: 10.1016/j.jfa.2024.110679

Jintao Deng , Liang Guo , Qin Wang , Guoliang Yu

Let ${(1 \to N_{n} \to G_{n} \to Q_{n} \to 1)}_{n \in N}$ be a sequence of extensions of finite groups. Assume that the coarse disjoint unions of ${(N_{n})}_{n \in N}$ , ${(G_{n})}_{n \in N}$ and ${(Q_{n})}_{n \in N}$ have bounded geometry. The sequence ${(G_{n})}_{n \in N}$ is said to have an FCE-by-FCE structure, if the sequence ${(N_{n})}_{n \in N}$ and the sequence ${(Q_{n})}_{n \in N}$ admit a fibred coarse embedding into Hilbert space. In this paper, we prove the coarse Novikov conjecture holds for the sequence ${(G_{n})}_{n \in N}$ with an FCE-by-FCE structure.

设（1→Nn→Gn→Qn→1）n∈N 是有限群的扩展序列。假设 (Nn)n∈N、(Gn)n∈N 和 (Qn)n∈N 的粗糙不相接的联合具有有界几何。如果序列(Nn)n∈N 和序列(Qn)n∈N 允许纤维粗嵌入到希尔伯特空间，则称序列(Gn)n∈N 具有 FCE-by-FCE 结构。本文证明了具有 FCE-by-FCE 结构的序列 (Gn)n∈N 的粗诺维科夫猜想成立。

引用次数: 0

Density of compactly supported smooth functions CC∞(Rd) in Musielak-Orlicz-Sobolev spaces W1,Φ(Ω) Musielak-Orlicz-Sobolev 空间 W1,Φ(Ω) 中紧凑支撑的光滑函数 CC∞(Rd)的密度

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-16 DOI: 10.1016/j.jfa.2024.110677

Anna Kamińska , Mariusz Żyluk

We investigate here the density of the set of the restrictions from

C_{C}^{\infty} (R^{d})

C_{C}^{\infty} (Ω)

in the Musielak-Orlicz-Sobolev space

W^{1, Φ} (Ω)

. It is a continuation of article [15], where we have studied density of

C_{C}^{\infty} (R^{d})

W^{k, Φ} (R^{d})

for

k \in N

. The main theorem states that for an open subset

Ω \subset R^{d}

with its boundary of class

C^{1}

, and Musielak-Orlicz function Φ satisfying condition (A1) which is a sort of log-Hölder continuity and the growth condition

Δ_{2}

, the set of restrictions of functions from

C_{C}^{\infty} (R^{d})

to Ω is dense in

W^{1, Φ} (Ω)

. We obtain a corresponding result in variable exponent Sobolev space

W^{1, p (\cdot)} (Ω)

under the assumption that the exponent

p (x)

is essentially bounded on Ω and

Φ (x, t) = t^{p (x)}

t \geq 0

x \in Ω

, satisfies the log-Hölder condition.

我们在此研究在 Musielak-Orlicz-Sobolev 空间 W1,Φ(Ω) 中从 CC∞(Rd)到 CC∞(Ω)的限制集的密度。这是文章[15]的继续，我们在文章[15]中研究了 k∈N 时 Wk,Φ(Rd) 中 CC∞(Rd)的密度。主定理指出，对于边界为 C1 类的开放子集 Ω⊂Rd，以及满足 log-Hölder 连续性条件 (A1) 和增长条件 Δ2 的 Musielak-Orlicz 函数 Φ，从 CC∞(Rd)到 Ω 的函数限制集在 W1,Φ(Ω) 中是密集的。假设指数 p(x) 在 Ω 上基本上是有界的且Φ(x,t)=tp(x), t≥0, x∈Ω, 满足 log-Hölder 条件，我们将在变指数 Sobolev 空间 W1,p(⋅)(Ω) 中得到相应的结果。

引用次数: 0

An integrable bound for rough stochastic partial differential equations with applications to invariant manifolds and stability 粗糙随机偏微分方程的可积分约束及其在不变流形和稳定性方面的应用

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-16 DOI: 10.1016/j.jfa.2024.110676

M. Ghani Varzaneh, S. Riedel

We study semilinear rough stochastic partial differential equations as introduced in Gerasimovičs and Hairer (2019) [31]. We provide $L^{p} (Ω)$ -integrable a priori bounds for the solution and its linearization in case the equation is driven by a suitable Gaussian process. Using the multiplicative ergodic theorem for Banach spaces, we can deduce the existence of a Lyapunov spectrum for the linearized equation around stationary points. The existence of local stable, unstable, and center manifolds around stationary points is provided. In the case where all Lyapunov exponents are negative, local exponential stability can be deduced. We illustrate our findings with several examples.

我们研究的是 Gerasimovičs 和 Hairer (2019) [31] 中引入的半线性粗糙随机偏微分方程。我们为方程由合适的高斯过程驱动时的解及其线性化提供了 Lp(Ω)-integrable 先验边界。利用巴拿赫空间的乘法遍历定理，我们可以推导出线性化方程在静止点附近存在李亚普诺夫谱。我们还提供了静止点周围存在的局部稳定流形、不稳定流形和中心流形。在所有 Lyapunov 指数都为负的情况下，可以推导出局部指数稳定性。我们用几个例子来说明我们的发现。

引用次数: 0

A probabilistic approach to Lorentz balls ℓq,1n 洛伦兹球 ℓq,1n 的概率方法

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-14 DOI: 10.1016/j.jfa.2024.110682

Zakhar Kabluchko , Joscha Prochno , Mathias Sonnleitner

We develop a probabilistic approach to study the volumetric and geometric properties of unit balls $B_{q, 1}^{n}$ of finite-dimensional Lorentz sequence spaces $ℓ_{q, 1}^{n}$ . More precisely, we show that the empirical distribution of a random vector $X^{(n)}$ uniformly distributed on its volume normalized unit ball converges weakly to a compactly supported symmetric probability distribution with explicitly given density; as a consequence we obtain a weak Poincaré-Maxwell-Borel principle for any fixed number $k \in N$ of coordinates of $X^{(n)}$ as $n \to \infty$ . Moreover, we prove a central limit theorem for the largest coordinate of $X^{(n)}$ , demonstrating a quite different behavior than in the case of the $ℓ_{q}^{n}$ balls, where a Gumbel distribution appears in the limit. Finally, we prove a Schechtman-Schmuckenschläger type result for the asymptotic volume of intersections of volume normalized $ℓ_{q, 1}^{n}$ and $ℓ_{p}^{n}$ balls.

我们开发了一种概率方法来研究有限维洛伦兹序列空间 ℓq,1n 的单位球 Bq,1n 的体积和几何特性。更确切地说，我们证明了均匀分布在其体积归一化单位球上的随机向量 X(n) 的经验分布弱收敛于具有明确给定密度的紧凑支撑对称概率分布；因此，我们得到了对于 X(n) 坐标的任意固定数 k∈N 的弱 Poincaré-Maxwell-Borel 原则，即 n→∞。此外，我们还证明了 X(n) 最大坐标的中心极限定理，证明了与ℓqn 球截然不同的行为，在ℓqn 球的极限中出现了冈贝尔分布。最后，我们证明了关于体积归一化 ℓq,1n 和 ℓpn 球交点的渐近体积的谢赫特曼-施穆克恩施拉格（Schechtman-Schmuckenschläger）式结果。

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引用次数: 0

Wave front sets of nilpotent Lie group representations 零能李群代表的波前集

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-14 DOI: 10.1016/j.jfa.2024.110684

Julia Budde, Tobias Weich

Let G be a nilpotent, connected, simply connected Lie group with Lie algebra

g

, and π a unitary representation of G. In this article we prove that the wave front set of π coincides with the asymptotic cone of the orbital support of π, i.e.

WF (π) = AC (⋃_{σ \in supp (π)} O_{σ})

, where

O_{σ} \subset i g^{⁎}

is the coadjoint Kirillov orbit associated to the irreducible unitary representation

σ \in \hat{G}

本文将证明 π 的波前集与π 的轨道支持的渐近锥重合，即 WF(π)=AC(⋃σ∈supp(π)Oσ, 其中 Oσig⁎ 是 coadointe 的 coadointe。即 WF(π)=AC(⋃σ∈supp(π)Oσ), 其中 Oσ⊂ig⁎ 是与不可减单元表示 σ∈Gˆ 相关联的共轭基里洛夫轨道。

引用次数: 0

Absolute continuity of degenerate elliptic measure 退化椭圆度量的绝对连续性

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-13 DOI: 10.1016/j.jfa.2024.110673

Mingming Cao , Kôzô Yabuta

Let

Ω \subset R^{n + 1}

be an open set whose boundary may be composed of pieces of different dimensions. Assume that Ω satisfies the quantitative openness and connectedness, and there exist doubling measures m on Ω and μ on ∂Ω with appropriate size conditions. Let

L u = - div (A \nabla u)

be a real (not necessarily symmetric) degenerate elliptic operator in Ω. Write

ω_{L}

for the associated degenerate elliptic measure. We establish the equivalence between the following properties: (i)

ω_{L} \in A_{\infty} (μ)

, (ii) the Dirichlet problem for L is solvable in

L^{p} (μ)

for some

p \in (1, \infty)

, (iii) every bounded null solution of L satisfies Carleson measure estimates with respect to μ, (iv) the conical square function is controlled by the non-tangential maximal function in

L^{q} (μ)

for all

q \in (0, \infty)

for any null solution of L, and (v) the Dirichlet problem for L is solvable in

BMO (μ)

. On the other hand, we obtain a qualitative analogy of the previous equivalence. Indeed, we characterize the absolute continuity of

ω_{L}

with respect to μ in terms of local

L^{2} (μ)

estimates of the truncated conical square function for any bounded null solution of L. This is also equivalent to the finiteness μ-almost everywhere of the truncated conical square function for any bounded null solution of L.

让 Ω⊂Rn+1 是一个开放集，其边界可能由不同维度的片段组成。假设Ω 满足定量开放性和连通性，且存在Ω 上的倍增度量 m 和∂Ω 上的倍增度量 μ，并有适当的大小条件。让 Lu=-div(A∇u) 是 Ω 中的实（不一定对称）退化椭圆算子。我们建立以下性质之间的等价关系：(i) ωL∈A∞(μ)；(ii) L 的 Dirichlet 问题在某个 p∈(1,∞)的 Lp(μ)中是可解的；(iii) L 的每个有界空解都满足关于 μ 的 Carleson 度量估计、(v) L 的 Dirichlet 问题在 BMO(μ) 中是可解的。另一方面，我们得到了前述等价性的定性类比。事实上，我们用 L 的任何有界空解的截锥平方函数的局部 L2(μ) 估计值来描述 ωL 关于 μ 的绝对连续性，这也等价于 L 的任何有界空解的截锥平方函数的有限性 μ-almost everywhere。

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引用次数: 0

Decay estimates for Beam equations with potential in dimension three 三维势能束方程的衰减估计值

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2024-09-13 DOI: 10.1016/j.jfa.2024.110671

Miao Chen , Ping Li , Avy Soffer , Xiaohua Yao

This paper is devoted to studying time decay estimates of the solution for Beam equation (higher order type wave equation) with a potential $u_{t t} + (Δ^{2} + V) u = 0, u (0, x) = f (x), u_{t} (0, x) = g (x)$ in dimension three, where V is a real-valued and decaying potential. Assume that zero is a regular point of $H = Δ^{2} + V$ , we first prove the following optimal time decay estimates of the solution operators ${‖ \cos (t \sqrt{H}) P_{a c} (H) ‖}_{L^{1} \to L^{\infty}} ≲ | t |^{- \frac{3}{2}} and {‖ \frac{\sin (t \sqrt{H})}{\sqrt{H}} P_{a c} (H) ‖}_{L^{1} \to L^{\infty}} ≲ | t |^{- \frac{1}{2}} .$ Moreover, if zero is a resonance of H, then time decay of the solution operators also is considered. It is noted that a first-kind resonance does not affect the decay rates of the propagator operators $\cos (t \sqrt{H})$ and $\frac{\sin (t \sqrt{H})}{\sqrt{H}}$ , but their decay will be significantly changed for the second and third-kind resonances.

本文致力于研究三维中具有势utt+(Δ2+V)u=0,u(0,x)=f(x),ut(0,x)=g(x)的梁方程（高阶型波方程）解的时间衰减估计，其中 V 为实值衰减势。假设零点是 H=Δ2+V 的正则点，我们首先证明以下解算子的最优时间衰减估计值‖cos(tH)Pac(H)‖L1→∞≲|t|-32 和‖sin(tH)HPac(H)‖L1→∞≲|t|-12。此外，如果零点是 H 的共振，则还要考虑解算子的时间衰减。我们注意到，第一类共振不会影响传播算子 cos(tH) 和 sin(tH)H 的衰减率，但它们的衰减在第二类和第三类共振时会发生显著变化。

引用次数: 0

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全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Functional Analysis

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