Journal of Functional Analysis最新文献

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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

An eternal hypersurface flow arising in centro-affine geometry 一种在中心仿射几何中产生的永恒的超表面流

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111347

Xinjie Jiang , Changzheng Qu , Yun Yang

In this paper, the existence and uniqueness for a specific centro-affine invariant hypersurface flow in

R^{n + 1}

are studied, and the corresponding evolutionary processes in both centro-affine and Euclidean settings are explored. It turns out that this flow exhibits similar properties to the standard heat flow. In addition, the long time existence of this flow is investigated, which shows that the hypersurface governed by this flow becomes asymptotically ellipsoidal via systematically investigating evolutions of centro-affine invariants. Furthermore, a classification of eternal solutions for this flow is provided.

本文研究了Rn+1中特定的中心仿射不变超表面流的存在唯一性，并探讨了相应的中心仿射和欧氏环境下的演化过程。结果表明，这种流动表现出与标准热流相似的性质。此外，研究了该流的长时间存在性，通过系统地研究中心仿射不变量的演化，表明受该流支配的超曲面渐近椭球面。进一步给出了该流的永恒解的分类。

引用次数: 0

Adelic C⁎-correspondences and parabolic induction Adelic C - C -对应和抛物线归纳

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-13 DOI: 10.1016/j.jfa.2026.111355

Magnus Goffeng , Bram Mesland , Mehmet Haluk Şengün

In analogy with the factorization of representations of adelic groups as restricted products of representations of local groups, we study restricted tensor products of Hilbert

C^{⁎}

-modules and of

C^{⁎}

-correspondences. The construction produces global

C^{⁎}

-correspondences from compatible collections of local

C^{⁎}

-correspondences. When applied to the collection of

C^{⁎}

-correspondences capturing local parabolic induction, the construction produces a global

C^{⁎}

-correspondence that captures adelic parabolic induction.

与将非对称群的表示分解为局部群的表示的限制积类似，我们研究了Hilbert C -模和C -对应的限制张量积。施工生产全球C⁎通讯从兼容的集合当地C⁎通讯。当应用于捕获局部抛物线感应的C -对应集合时，该构造产生捕获非抛物线感应的全局C -对应。

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

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 : 2026-01-12 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

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

Instability of the fundamental group for non-collapsed Ricci-limits 非塌缩ricci极限下基本群的不稳定性

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-09 DOI: 10.1016/j.jfa.2026.111343

Camillo Brena

We construct two sequences of closed 4-dimensional manifolds with non-negative Ricci curvature, diameter bounded from above by 1, and volume bounded from below by

v > 0

, with different fundamental groups but with the same Gromov–Hausdorff limit. This provides a negative answer to the question posed in J. Pan (2025) [9].

构造了两个非负Ricci曲率的封闭四维流形序列，它们具有不同的基本群，但具有相同的Gromov-Hausdorff极限，其直径上界为1，体积下界为v>；0。这为J. Pan (2025) b[9]提出的问题提供了一个否定的答案。

引用次数: 0

Differential symmetry breaking operators for the pair (GLn+1(R),GLn(R)) 对(GLn+1（R),GLn(R)）的微分对称破缺算子

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-06 DOI: 10.1016/j.jfa.2025.111335

Jonathan Ditlevsen , Quentin Labriet

In this article we study differential symmetry breaking operators between principal series representations induced from minimal parabolic subgroups for the pair

({GL}_{n + 1} (R), {GL}_{n} (R))

. Using the source operator philosophy we construct such operators for generic induction parameters of the representations and establish that this approach yields all possible operators in this setting. We show that these differential operators occur as residues of a family of symmetry breaking operators that depends meromorphically on the parameters. Finally, in the

n = 2

case we classify and construct all differential symmetry breaking operators for any parameters, including the non-generic ones.

本文研究了最小抛物子群对(GLn+1（R),GLn(R)）的主级数表示之间的微分对称破缺算子。使用源算子哲学，我们为表示的一般归纳参数构造这样的算子，并确定这种方法产生这种设置中的所有可能的算子。我们证明了这些微分算子是亚纯依赖于参数的对称破缺算子族的残数。最后，在n=2的情况下，我们对任意参数的所有微分对称破缺算子进行了分类和构造，包括非泛型的微分对称破缺算子。

引用次数: 0

Qualitative analysis for ground state solutions of logarithmic Schrödinger equations under a small constant magnetic field in RN 小恒磁场作用下对数Schrödinger方程基态解的定性分析

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-01-06 DOI: 10.1016/j.jfa.2025.111333

Xiaoming An , Shuangjie Peng , Xian Yang , Fulin Zhong

We consider the qualitative properties of ground states of the logarithmic Schrödinger equation with magnetic fields

{(i \nabla + b x^{⊥})}^{2} u = u \log | u | in R^{N},

where

N = 2, 3

, b is a real constant,

x^{⊥} = (- x_{2}, x_{1}, 0)

N = 3

and

(- x_{2}, x_{1})

N = 2

is derived from the magnetic field B in the relation

\nabla \times A = B

. We obtain a ground state solution to the problem by revealing the relation between this equation and the power-law Schrödinger equation

{(i \nabla + b x^{⊥})}^{2} u + u = | u |^{p - 2} u

. For sufficiently small

| b |

, we also demonstrate that the ground state solutions are positive and nondegenerate. Moreover, they are unique and radially symmetric up to magnetic translations and rotations in the complex phase space.

我们考虑对数Schrödinger方程的基态的定性性质，该方程具有磁场（i∇+bx⊥）2u=ulog (|u|inRN，其中N=2,3， b是实常数，如果N=3，则x⊥=(- x2,x1,0)，如果N=2，则（- x2,x1）是从关系∇×A= b中的磁场b推导出来的。通过揭示该方程与幂律Schrödinger方程（i∇+bx⊥）2u+u=|u|p−2u之间的关系，我们获得了该问题的基态解。对于足够小的|b|，我们还证明了基态解是正的和非简并的。此外，它们是唯一的和径向对称的，直到磁平移和旋转在复相空间。

引用次数: 0

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