Journal of Functional Analysis最新文献

英文中文

On von Neumann algebras generated by free Poisson random weights 自由泊松随机权生成的von Neumann代数

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-04-15 Epub Date: 2026-01-13 DOI: 10.1016/j.jfa.2026.111358

Zhiyuan Yang

We study a generalization of free Poisson random measure by replacing the intensity measure with a n.s.f. weight φ on a von Neumann algebra M. We give an explicit construction of the free Poisson random weight using full Fock space over the Hilbert space

L^{2} (M, φ)

and study the free Poisson von Neumann algebra

Γ (M, φ)

generated by this random weight. This construction can be viewed as a free Poisson type functor for left Hilbert algebras similar to Voiculescu's free Gaussian functor for Hilbert spaces. When

φ (1) < \infty

, we show that

Γ (M, φ)

can be decomposed into free product of other algebras. For a general weight φ, we prove that

Γ (M, φ)

is a factor if and only if

φ (1) \geq 1

and

M \neq C

. The second quantization of subunital weight decreasing completely positive maps is studied. By considering a degenerate version of left Hilbert algebras, we are also able to treat free Araki-Woods algebras as special cases of free Poisson algebras for degenerate left Hilbert algebras. We show that the Lévy-Itô decomposition of a jointly freely infinitely divisible family (in a tracial probability space) can in fact be interpreted as a decomposition of a degenerate left Hilbert algebra. Finally, as an application, we give a realization of any additive time-parameterized free Lévy process as unbounded operators in a full Fock space. Using this realization, we show that the filtration algebras of any additive free Lévy process are always interpolated group factors with a possible additional atom.

在Hilbert空间L2（M,φ）上利用满Fock空间给出了自由泊松随机权的显式构造，并研究了由该随机权生成的自由泊松von Neumann代数Γ（M,φ）。这种构造可以看作是左希尔伯特代数的自由泊松型函子，类似于Voiculescu的希尔伯特空间的自由高斯函子。当φ(1)<；∞时，我们证明Γ（M,φ）可以分解为其它代数的自由积。对于一般权值φ，证明Γ（M,φ）是因子当且仅当φ(1)≥1且M≠C。研究了亚单位权递减完全正映射的二次量化问题。通过考虑左希尔伯特代数的退化版本，我们也能够将自由Araki-Woods代数视为退化左希尔伯特代数的自由泊松代数的特殊情况。我们证明了联合自由无限可分族（在迹概率空间中）的Lévy-Itô分解实际上可以解释为退化的左希尔伯特代数的分解。最后，作为应用，我们给出了在满Fock空间中任意加性时参数化自由lsamvy过程作为无界算子的实现。利用这一实现，我们证明了任何可加自由lsamvy过程的过滤代数都是内插的群因子，并可能有一个额外的原子。

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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 : 2026-04-15 Epub 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

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 : 2026-04-15 Epub 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

Contractive realization theory for the annulus and other intersections of disks on the Riemann sphere 黎曼球上盘的环和其他交点的收缩实现理论

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-04-15 Epub Date: 2026-01-12 DOI: 10.1016/j.jfa.2026.111346

Radomił Baran , Piotr Pikul , Hugo J. Woerdeman , Michał Wojtylak

We develop contractive finite dimensional realizations for rational matrix functions of one variable on domains that are not simply connected, such as the annulus. The proof uses multivariable contractive realization results as well as abstract operator algebra techniques. Other results include new bounds for the Bohr radius of the bidisk and the annulus.

我们开发了非单连通域上一元有理矩阵函数的有限维压缩实现，如环空。该证明采用了多变量压缩实现结果和抽象算子代数技术。其他结果包括双盘和环的玻尔半径的新界限。

引用次数: 0

An isoperimetric inequality for lower order Neumann eigenvalues in Gauss space 高斯空间中低阶诺伊曼特征值的等周不等式

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-04-15 Epub Date: 2026-01-22 DOI: 10.1016/j.jfa.2026.111379

Yi Gao, Kui Wang

We prove a sharp isoperimetric inequality for the harmonic mean of the first

m - 1

nonzero Neumann eigenvalues for Lipschitz domains symmetric about the origin in Gauss space. Our result generalizes the Szegö-Weinberger type inequality in Gauss space, which was proven by Chiacchio and Di Blasio in [12, Theorem 4.1].

我们证明了高斯空间中关于原点对称的Lipschitz域的前m−1个非零诺伊曼特征值的调和平均值的尖锐等周不等式。我们的结果推广了高斯空间中由Chiacchio和Di Blasio在[12，定理4.1]中证明的Szegö-Weinberger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 : 2026-04-15 Epub 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

The free boundary for a superlinear system 超线性系统的自由边界

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-04-15 Epub Date: 2026-01-21 DOI: 10.1016/j.jfa.2026.111363

Daniela De Silva , Seongmin Jeon , Henrik Shahgholian

In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional

\int_{Ω} (| \nabla u |^{2} + \frac{2}{p} | u |^{p}), 0 < p < 1,

but solutions can be also understood in an ad hoc viscosity way.

First, we prove the optimal regularity of minimizers using a variational approach. Then, we apply a linearization technique to establish the

C^{1, α}

-regularity of the “flat” part of the free boundary via a viscosity method. Finally, for minimizing free boundaries, we extend this result to analyticity.

本文研究了产生自由边界的超线性系统。例如，这样的系统出现在能量泛函∫Ω（|∇u|2+2p|u|p），0<p<；1的最小化中，但解也可以用一种特殊的粘度方式来理解。首先，我们用变分方法证明了最小值的最优正则性。然后，我们应用线性化技术，通过粘度法建立了自由边界“平坦”部分的C1，α-正则性。最后，对于最小化自由边界，我们将这一结果推广到可分析性。

引用次数: 0

K-theory and structural properties of C⁎-algebras associated with relative generalized Boolean dynamical systems 与相对广义布尔动力系统相关的C -代数的k理论和结构性质

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-04-15 Epub Date: 2026-01-21 DOI: 10.1016/j.jfa.2026.111348

Toke Meier Carlsen , Eun Ji Kang

We present an explicit formula for the K-theory of the

C^{⁎}

-algebra associated with a relative generalized Boolean dynamical system

(B, L, θ, I_{α}; J)

. In particular, we find concrete generators for the

K_{1}

-group of

C^{⁎} (B, L, θ, I_{α}; J)

. We also prove that every gauge-invariant ideal of

C^{⁎} (B, L, θ, I_{α}; J)

is Morita equivalent to a

C^{⁎}

-algebra of a relative generalized Boolean dynamical system.

As a structural application, we show that if the underlying Boolean dynamical system

(B, L, θ)

satisfies Condition (K), then the associated

C^{⁎}

-algebra is

K_{0}

-liftable. Furthermore, we deduce that if

C^{⁎} (B, L, θ, I_{α}; J)

is separable and purely infinite, then it has real rank zero.

我们给出了与相对广义布尔动力系统（B，L,θ,Iα；J）相关的C -代数的k理论的一个显式公式。特别地，我们找到了C _ （B，L,θ,Iα；J）的k1群的具体发生器。我们还证明了C （B，L,θ,Iα；J）的每一个规范不变理想都是Morita等价于一个相对广义布尔动力系统的C代数。作为一个结构应用，我们证明了如果底层布尔动力系统（B，L,θ）满足条件(K)，则相关的C -代数是k0可举的。进一步，我们推导出，如果C - C （B，L,θ, i - α；J）是可分离的纯无限的，那么它的实秩为零。

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 : 2026-04-15 Epub 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。

{"title":"Non-strict singularity of optimal Sobolev embeddings","authors":"Jan Lang , Zdeněk Mihula","doi":"10.1016/j.jfa.2026.111344","DOIUrl":"10.1016/j.jfa.2026.111344","url":null,"abstract":"<div><div>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).</div><div>More specifically, we focus on studying the “quality” of non-compactness for optimal Sobolev embeddings <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>m</mi></mrow></msubsup><mi>X</mi><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>→</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>, where <em>X</em> is a given r.i. space and <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is the corresponding optimal target r.i. space (i.e., the smallest among all r.i. spaces).</div><div>For the class of sub-limiting norms (i.e., the norms whose fundamental function satisfies <span><math><msub><mrow><mi>φ</mi></mrow><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>X</mi></mrow></msub></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>≈</mo><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mi>m</mi><mo>/</mo><mi>n</mi></mrow></msup><msub><mrow><mi>φ</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> as <span><math><mi>t</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span>), 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.</div><div>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 <span><math><mi>X</mi><mo>=</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>w</mi></mrow><mrow><mi>q</mi></mrow></msubsup></math></span>, <span><math><mi>q</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>. Except for the endpoint case <span><math><mi>X</mi><mo>=</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>/</mo><mi>m</mi><mo>,</mo><mn>1</mn></mrow></msup></math></span>, our spike-function construction enables us to construct a subspace of <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>m</mi></mrow></msubsup><mi>X</mi></math></span> that is isomorphic to <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>, which we then leverage to prove the non-strict singularity of the corresponding optimal Sobolev embedding.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111344"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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 : 2026-04-15 Epub 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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