Journal of Functional Analysis最新文献

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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 : 2026-05-01 Epub 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

Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem 具有部分DMO系数的退化或奇异抛物型系统：狄利克雷问题

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-22 DOI: 10.1016/j.jfa.2026.111365

Hongjie Dong , Seongmin Jeon

In this paper, we study solutions u of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder

Q_{1}^{+} \subset R^{n + 1}

, where the coefficients are weighted by

x_{n}^{α}

α \in (- \infty, 1)

. We establish higher-order boundary Schauder type estimates of

x_{n}^{α} u

under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with Hölder continuous coefficients.

本文研究了上半圆柱体Q1+∧Rn+1中Dirichlet边界条件为零的发散型抛物型方程组的解u，其中系数用xnα， α∈(−∞,1)加权。在系数部分具有Dini平均振荡的假设下，建立了xnαu的高阶边界Schauder型估计。作为应用，我们也得到了具有Hölder连续系数的退化或奇异方程的高阶边界哈纳克原理。

引用次数: 0

Half-space Liouville-type theorems for minimal graphs with capillary boundary 具有毛细边界的极小图的半空间liouville型定理

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-21 DOI: 10.1016/j.jfa.2026.111366

Guofang Wang , Wei Wei , Xuwen Zhang

In this paper, we prove two Liouville-type theorems for capillary minimal graph over

R_{+}^{n}

. First, if u has linear growth, then for

n = 2, 3

and for any

θ \in (0, π)

, or

n \geq 4

and

θ \in (\frac{π}{6}, \frac{5 π}{6})

, u must be flat. Second, if u is one-sided bounded on

R_{+}^{n}

, then for any n and

θ \in (0, π)

, u must be flat. The proofs build upon gradient estimates for the mean curvature equation over

R_{+}^{n}

with capillary boundary condition, which are based on carefully adapting the maximum principle to the capillary setting.

本文证明了R+n上毛细极小图的两个liouville型定理。首先，如果u具有线性增长，则对于n=2,3，对于任意θ∈(0,π)，或n≥4且θ∈(π6,5π6)， u必须是平坦的。第二，如果u在R+n上是单侧有界的，那么对于任意n和θ∈(0,π)， u一定是平的。这些证明建立在具有毛细管边界条件的R+n上的平均曲率方程的梯度估计的基础上，该梯度估计是基于仔细地将极大值原理应用于毛细管设置。

引用次数: 0

On the log-Sobolev constant of log-concave vectors 关于log-Sobolev常数的对数凹向量

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2026-05-01 Epub Date: 2026-01-21 DOI: 10.1016/j.jfa.2026.111368

Pierre Bizeul

It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whether this implication can be reversed under a log-concavity assumption. In the general setting, we improve on a result of Bobkov, establishing the best dimension dependent bound on the log-Sobolev constant of subgaussian log-concave measures, and we investigate some special cases.

众所周知，如果一个随机向量满足log-Sobolev不等式，它的所有边际都有亚高斯尾。在KLS猜想的精神下，我们研究了在对数凹性假设下是否可以反转这一含义。在一般情况下，我们改进了Bobkov的结果，建立了亚高斯对数凹测度的log-Sobolev常数的最佳维数依赖界，并研究了一些特殊情况。

引用次数: 0

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 : 2026-05-01 Epub 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 : 2026-05-01 Epub 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

Global well-posedness and density patches for liquid crystal system 液晶系统的全局适定性和密度补丁

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.2026.111356

Qionglei Chen , Xiaonan Hao , Omar Lazar

We prove a global well-posedness result for a liquid crystal system with bounded but arbitrarily large density and velocity. Applying the Lagrangian approach with more refined estimates we are able to not only work in the critical regularity space but also to overcome the difficulty arising from the fact that we are dealing with a coupled hyperbolic system. Taking advantage of our uniqueness result, we study the density patches problem by using classical techniques, namely, Littlewood-Paley multipliers together with the smoothing effect of the Newtonian potential and on certain symmetry property motivated by [13]. One of the key point of the proof is to introduce the material derivative and perform more refined estimates for the direction field.

我们证明了具有有界但任意大密度和速度的液晶系统的全局适定性结果。应用拉格朗日方法和更精细的估计，我们不仅能够在临界正则性空间中工作，而且能够克服由于我们处理耦合双曲系统而产生的困难。利用我们的唯一性结果，我们利用经典的方法，即Littlewood-Paley乘法器，结合牛顿势的平滑效应，以及[13]驱动下的某种对称性，研究了密度斑块问题。证明的关键之一是引入物质导数，对方向场进行更精细的估计。

引用次数: 0

A note on the stability of self-similar blow-up solutions for superconformal semilinear wave equations 超共形半线性波动方程自相似爆破解的稳定性注记

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.2026.111364

Jie Liu

In this note, we investigate the stability of self-similar blow-up solutions for superconformal semilinear wave equations in all dimensions. A central aspect of our analysis is the spectral equivalence of the linearized operators under Lorentz transformations in self-similar variables. This observation serves as a useful tool in proving mode stability and provides insights that may aid the study of self-similar solutions in related problems. As a direct consequence, we establish the asymptotic stability of the ODE blow-up family, extending the classical results of Merle and Zaag [45], [51] to the conformal and superconformal regimes and generalizing the recent work of Ostermann [52] to include the entire ODE blow-up family.

本文研究了超共形半线性波动方程自相似爆破解在所有维度上的稳定性。我们分析的一个中心方面是自相似变量中洛伦兹变换下线性化算子的谱等价性。这一观察结果是证明模态稳定性的有用工具，并提供了有助于研究相关问题中自相似解的见解。作为直接结果，我们建立了ODE爆破族的渐近稳定性，将Merle和Zaag[45]，[51]的经典结果推广到共形和超共形区域，并将Ostermann[52]的最新工作推广到包括整个ODE爆破族。

引用次数: 0

Conformal and extrinsic upper bounds for the harmonic mean of Neumann and Steklov eigenvalues Neumann和Steklov特征值调和平均值的共形和外在上界

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.2026.111361

Hang Chen

Let M be an m-dimensional compact Riemannian manifold with boundary. We obtain the upper bounds of the harmonic mean of the first m nonzero Neumann eigenvalues and Steklov eigenvalues involving the conformal volume and relative conformal volume, respectively. We also give an optimal sharp extrinsic upper bound for closed submanifolds in space forms. These extend the previous related results for the first nonzero eigenvalues.

设M是一个有边界的M维紧致黎曼流形。我们分别得到了涉及共形体积和相对共形体积的前m个非零Neumann特征值和Steklov特征值的调和平均值的上界。我们还给出了空间形式的闭子流形的最优尖锐外部上界。这些扩展了先前关于第一个非零特征值的相关结果。

引用次数: 0

Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term 具有奇异非齐次项的分数阶半线性热方程解的存在性

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.2026.111352

Kazuhiro Ishige , Tatsuki Kawakami , Ryo Takada

We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces. Furthermore, we apply the real interpolation method in uniformly local Zygmund spaces to obtain sharp integral estimates on the inhomogeneous term and the nonlinear term. This enables us to find sharp sufficient conditions for the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term.

研究了一类具有奇异非齐次项的分数阶半线性热方程解的存在性。为此，我们建立了若干一致局部Zygumnd空间中分数阶热半群的衰减估计。进一步，我们在一致局部Zygmund空间中应用实插值方法，得到了非齐次项和非线性项的尖锐积分估计。这使我们能够找到具有奇异非齐次项的分数阶半线性热方程解存在的充分条件。

引用次数: 0

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