Proceedings of the Edinburgh Mathematical Society最新文献

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Inhomogeneous Poisson processes in the disk and interpolation 圆盘中的非均质泊松过程和插值法

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-30 DOI: 10.1017/s0013091524000282

Andreas Hartmann, Xavier Massaneda

We investigate different geometrical properties, related to Carleson measures and pseudo-hyperbolic separation, of inhomogeneous Poisson point processes on the unit disk. In particular, we give conditions so that these random sequences are almost surely interpolating for the Hardy, Bloch or weighted Dirichlet spaces.

我们研究了单位圆盘上不均匀泊松点过程的不同几何性质，这些性质与卡列松量度和伪双曲分离有关。特别是，我们给出了一些条件，使得这些随机序列对于哈代、布洛赫或加权德里赫利空间几乎肯定是插值的。

引用次数: 0

Weak amenability for dual Banach algebras 对偶巴拿赫代数的弱可配性

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-29 DOI: 10.1017/s0013091524000300

Amin Mahmoodi

A suitable notion of weak amenability for dual Banach algebras, which we call weak Connes amenability, is defined and studied. Among other things, it is proved that the measure algebra M(G) of a locally compact group G is always weakly Connes amenable. It can be a complement to Johnson’s theorem that $L^1(G)$ is always weakly amenable [10].

我们定义并研究了对偶巴拿赫代数的一个合适的弱可亲和性概念，我们称之为弱康恩可亲和性。除其他外，我们还证明了局部紧凑群 G 的度量代数 M(G) 总是弱康恩可亲和性的。它可以作为约翰逊关于 $L^1(G)$ 总是弱可朋性定理的补充[10]。

引用次数: 0

Projectively and affinely invariant PDEs on hypersurfaces 超曲面上的投影不变和仿射不变 PDEs

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-25 DOI: 10.1017/s0013091524000233

Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno

In Communications in Contemporary Mathematics24 3, (2022),the authors have developed a method for constructing G-invariant partial differential equations (PDEs) imposed on hypersurfaces of an $(n+1)$ -dimensional homogeneous space $G/H$ , under mild assumptions on the Lie group G. In the present paper, the method is applied to the case when $G=mathsf{PGL}(n+1)$ (respectively, $G=mathsf{Aff}(n+1)$ ) and the homogeneous space $G/H$ is the $(n+1)$ -dimensional projective $mathbb{P}^{n+1}$ (respectively, affine $mathbb{A}^{n+1}$ ) space, respectively. The main result of the paper is that projectively or affinely invariant PDEs with n independent and one unknown variables are in one-to-one correspondence with invariant hypersurfaces of the space of trace-free cubic forms</jats:itali

在Communications in Contemporary Mathematics24 3, (2022)一文中，作者提出了一种方法，用于在对Lie群G的温和假设下，构造施加于$(n+1)$维均质空间$G/H$的超曲面上的G不变偏微分方程（PDEs）。本文将该方法分别应用于 $G=mathsf{PGL}(n+1)$ （分别为 $G=mathsf{Aff}(n+1)$ ）和均相空间 $G/H$ 为 $(n+1)$ 维投影 $mathbb{P}^{n+1}$ （分别为仿射 $mathbb{A}^{n+1}$ ）空间的情况。本文的主要结果是，具有 n 个独立未知变量的投影或仿射不变 PDE 与 n 变量无迹三次方形式空间的不变超曲面一一对应，且与 $mathbb{R}^{d,n-d}$ 的共形变换组 $mathsf{CO}(d,n-d)$ 有关。

引用次数: 0

Annihilators and decompositions of singularity categories 奇点范畴的湮没器和分解

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-23 DOI: 10.1017/s001309152400018x

Özgür Esentepe, Ryo Takahashi

Given any commutative Noetherian ring R and an element x in R, we consider the full subcategory

$mathsf{C}(x)$

of its singularity category consisting of objects for which the morphism that is given by the multiplication by x is zero. Our main observation is that we can establish a relation between

$mathsf{C}(x), mathsf{C}(y)$

and

$mathsf{C}(xy)$

for any two ring elements x and y. Utilizing this observation, we obtain a decomposition of the singularity category and consequently an upper bound on the dimension of the singularity category.

给定任何交换诺特环 R 和 R 中的元素 x，我们考虑其奇异性范畴的全子范畴 $mathsf{C}(x)$ ，这个子范畴由 x 乘以的态量为零的对象组成。我们的主要观察结果是，对于任意两个环元素 x 和 y，我们可以在 $mathsf{C}(x), mathsf{C}(y)$ 和 $mathsf{C}(xy)$ 之间建立一种关系。

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引用次数: 0

Propagation of anisotropic Gabor wave front sets 各向异性 Gabor 波前集的传播

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-22 DOI: 10.1017/s0013091524000269

Patrik Wahlberg

We show a result on propagation of the anisotropic Gabor wave front set for linear operators with a tempered distribution Schwartz kernel. The anisotropic Gabor wave front set is parametrized by a positive parameter relating the space and frequency variables. The anisotropic Gabor wave front set of the Schwartz kernel is assumed to satisfy a graph type criterion. The result is applied to a class of evolution equations that generalizes the Schrödinger equation for the free particle. The Laplacian is replaced by any partial differential operator with constant coefficients, real symbol and order at least two.

我们展示了一个关于各向异性 Gabor 波前集传播的结果，该结果适用于具有调和分布 Schwartz 内核的线性算子。各向异性 Gabor 波前集的参数是空间和频率变量之间的正参数。假设 Schwartz 核的各向异性 Gabor 波前集满足图形类型标准。这一结果被应用于一类演化方程，该方程概括了自由粒子的薛定谔方程。拉普拉斯算子由任何具有常数系数、实符号和至少二阶的偏微分算子代替。

引用次数: 0

Pushforward of structure sheaf and virtual global generation 结构剪切的前推和虚拟全局生成

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-18 DOI: 10.1017/s001309152400021x

Indranil Biswas, Manish Kumar, A. J. Parameswaran

Let $f,:,X,longrightarrow ,Y$ be a generically smooth morphism between irreducible smooth projective curves over an algebraically closed field of arbitrary characteristic. We prove that the vector bundle $((f_*{mathcal O}_X)/{mathcal O}_Y)^*$ is virtually globally generated. Moreover, $((f_*{mathcal O}_X)/{mathcal O}_Y)^*$ is ample if and only if f is genuinely ramified.

让$f,:,X,longrightarrow ,Y$是任意特征的代数闭域上不可还原光滑投影曲线之间的一般光滑变形。我们证明向量束 $((f_*{mathcal O}_X)/{mathcal O}_Y)^*$ 实际上是全局生成的。此外，$((f_*{/mathcal O}_X)/{mathcal O}_Y)^*$ 是充裕的，当且仅当 f 是真正夯实的。

引用次数: 0

A remark on a conjecture on the symmetric Gaussian problem 关于对称高斯问题猜想的评论

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-15 DOI: 10.1017/s0013091524000221

Nicola Fusco, Domenico Angelo La Manna

In this paper, we study the functional given by the integral of the mean curvature of a convex set with Gaussian weight with Gaussian volume constraint. It was conjectured that the ball centred at the origin is the only minimizer of such a functional for certain values of the mass. We prove that this is the case in dimension 2 while in higher dimension the situation is different. In fact, for small values of mass, the ball centred at the origin is a local minimizer, while for larger values the ball is a maximizer among convex sets with a uniform bound on the curvature.

在本文中，我们研究了具有高斯体积约束的高斯权重凸集的平均曲率积分所给出的函数。有人猜想，对于某些质量值，以原点为中心的球是该函数的唯一最小值。我们证明在维度 2 中情况确实如此，而在更高维度中情况则不同。事实上，对于较小的质量值，以原点为中心的球是局部最小值，而对于较大的质量值，球在曲率有均匀约束的凸集中是最大值。

引用次数: 0

On the fractional powers of a Schrödinger operator with a Hardy-type potential 关于具有哈迪型势能的薛定谔算子的分数幂

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-12 DOI: 10.1017/s0013091524000063

Giovanni Siclari

Strong unique continuation properties and a classification of the asymptotic profiles are established for the fractional powers of a Schrödinger operator with a Hardy-type potential, by means of an Almgren monotonicity formula combined with a blow-up analysis.

通过阿尔姆格伦单调性公式与吹胀分析相结合的方法，为具有哈迪型势能的薛定谔算子的分数幂建立了强唯一延续特性和渐近剖面分类。

引用次数: 0

Normalized solutions to the quasilinear Schrödinger equations with combined nonlinearities 具有组合非线性的准线性薛定谔方程的归一化解

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-12 DOI: 10.1017/s001309152400004x

Anmin Mao, Shuyao Lu

We consider the radially symmetric positive solutions to quasilinear problem

begin{equation*}-triangle u-utriangle u^{2}+lambda u=f(u),quad{rm in} mathbb{R}^{N},end{equation*}

having prescribed mass

$int_{mathbb{R}^{N}}|u|^2 =a^2,$

where a > 0 is a constant, λ appears as a Lagrange multiplier. We focus on the pure L2-supercritical case and combination case of L2-subcritical and L2-supercritical nonlinearities

begin{equation*}f(u)=tau |u|^{q-2}u+|u|^{p-2}u,quad tau gt 0,qquad{rm where} 2 lt q lt 2+frac{4}{N} {rm and} quad p gt bar{p},end{equation*}

where

$bar{p}:=4+frac{4}{N}$

is the L2-critical exponent. Our work extends and develops some recent results in the literature.

我们考虑准线性问题的径向对称正解。mathbb{R}^{N},end{equation*} 具有规定质量 $int_{mathbb{R}^{N}}|u|^2 =a^2,$ 其中 a > 0 是常数，λ 作为拉格朗日乘数出现。我们重点讨论纯 L2 超临界情况以及 L2 超临界和 L2 超临界非线性的组合情况（begin{equation*}f(u)=tau |u|^{q-2}u+|u|^{p-2}u,quad tau gt 0,qquad{rm where} 2 lt q lt 2+frac{4}{N} 和quad p gt bar{p},end{equation*} 其中 $bar{p}:=4+frac{4}{N}$ 是 L2 临界指数。我们的工作扩展并发展了文献中的一些最新成果。

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引用次数: 0

Discriminant and integral basis of number fields defined by exponential Taylor polynomials 指数泰勒多项式定义的数域的判别和积分基础

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society

Pub Date : 2024-04-08 DOI: 10.1017/s0013091524000105

Ankita Jindal, Sudesh K. Khanduja

Let

$K_n=mathbb{Q}(alpha_n)$

be a family of algebraic number fields where

$alpha_nin mathbb{C}$

is a root of the nth exponential Taylor polynomial

$frac{x^n}{n!}+ frac{x^{n-1}}{(n-1)!}+ cdots +frac{x^2}{2!}+frac{x}{1!}+1$

$nin mathbb{N}$

. In this paper, we give a formula for the exact power of any prime p dividing the discriminant of Kn in terms of the p-adic expansion of n. An explicit p-integral basis of Kn is also given for each prime p. These p-integral bases quickly lead to the construction of an integral basis of Kn.

让 $K_n=mathbb{Q}(alpha_n)$ 是一个代数数域族，其中 $alpha_nin mathbb{C}$ 是第 n 次指数泰勒多项式 $frac{x^n}{n！}+ （frac{x^{n-1}}{(n-1)!}+ （cdots +frac{x^2}{2!}+frac{x}{1!}+1$ , $nin mathbb{N}$。在本文中，我们用 n 的 p-adic 扩展给出了除以 Kn 的判别式的任何素数 p 的精确幂的公式。这些 p 积分基很快就能导致 Kn 积分基的构建。

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引用次数: 0

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