Proceedings of the Edinburgh Mathematical Society最新文献_第7页

A Weakened Markus–Yamabe Condition for Planar Polynomial Differential Systems of Degree 平面多项式次微分系统的弱化Markus-Yamabe条件

3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-10-17 DOI: 10.1017/s0013091523000615

Jaume Llibre, Claudia Valls

引用次数: 0

On Weakly Almost Square Banach Spaces 弱几乎平方Banach空间

3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-10-05 DOI: 10.1017/s0013091523000536

José RodrÍguez, Abraham Rueda Zoca

{"title":"On Weakly Almost Square Banach Spaces","authors":"José RodrÍguez, Abraham Rueda Zoca","doi":"10.1017/s0013091523000536","DOIUrl":"https://doi.org/10.1017/s0013091523000536","url":null,"abstract":"Abstract We prove some results on weakly almost square Banach spaces and their relatives. On the one hand, we discuss weak almost squareness in the setting of Banach function spaces. More precisely, let $(Omega,Sigma)$ be a measurable space, let E be a Banach lattice and let $nu:Sigma to E^+$ be a non-atomic countably additive measure having relatively norm compact range. Then the space $L_1(nu)$ is weakly almost square. This result applies to some abstract Cesàro function spaces. Similar arguments show that the Lebesgue–Bochner space $L_1(mu,Y)$ is weakly almost square for any Banach space Y and for any non-atomic finite measure µ . On the other hand, we make some progress on the open question of whether there exists a locally almost square Banach space, which fails the diameter two property. In this line, we prove that if X is any Banach space containing a complemented isomorphic copy of c 0 , then for every $0 lt varepsilon lt 1$ , there exists an equivalent norm $|cdot|$ on X satisfying the following: (i) every slice of the unit ball $B_{(X,|cdot|)}$ has diameter 2; (ii) $B_{(X,|cdot|)}$ contains non-empty relatively weakly open subsets of arbitrarily small diameter and (iii) $(X,|cdot|)$ is ( r , s )-SQ for all $0 lt r,s lt frac{1-varepsilon}{1+varepsilon}$ .","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134976021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Discrete restriction estimates for forms in many variables 多变量形式的离散约束估计

3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-09-18 DOI: 10.1017/s0013091523000366

Brian Cook, Kevin Hughes, Eyvindur Palsson

引用次数: 0

Perron’s capacity of random sets 随机集的Perron容量

IF 0.7 3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-09-01 DOI: 10.1017/s0013091523000482

A. Gauvan

引用次数: 0

PEM series 2 volume 66 issue 3 Cover and Back matter PEM系列2卷66期3封面和封底

IF 0.7 3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-08-01 DOI: 10.1017/s0013091523000524

引用次数: 0

On the density of bounded bases 关于有界基的密度

IF 0.7 3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-08-01 DOI: 10.1017/S0013091523000421

Jin-Hui Fang

{"title":"On the density of bounded bases","authors":"Jin-Hui Fang","doi":"10.1017/S0013091523000421","DOIUrl":"https://doi.org/10.1017/S0013091523000421","url":null,"abstract":"Abstract For a nonempty set A of integers and an integer n, let $r_{A}(n)$ be the number of representations of n in the form $n=a+a'$, where $aleqslant a'$ and $a, a'in A$, and $d_{A}(n)$ be the number of representations of n in the form $n=a-a'$, where $a, a'in A$. The binary support of a positive integer n is defined as the subset S(n) of nonnegative integers consisting of the exponents in the binary expansion of n, i.e., $n=sum_{iin S(n)} 2^i$, $S(-n)=-S(n)$ and $S(0)=emptyset$. For real number x, let $A(-x,x)$ be the number of elements $ain A$ with $-xleqslant aleqslant x$. The famous Erdős-Turán Conjecture states that if A is a set of positive integers such that $r_A(n)geqslant 1$ for all sufficiently large n, then $limsup_{nrightarrowinfty}r_A(n)=infty$. In 2004, Nešetřil and Serra initially introduced the notation of “bounded” property and confirmed the Erdős-Turán conjecture for a class of bounded bases. They also proved that, there exists a set A of integers satisfying $r_A(n)=1$ for all integers n and $|S(x)bigcup S(y)|leqslant 4|S(x+y)|$ for $x,yin A$. On the other hand, Nathanson proved that there exists a set A of integers such that $r_A(n)=1$ for all integers n and $2log x/log 5+c_1leqslant A(-x,x)leqslant 2log x/log 3+c_2$ for all $xgeqslant 1$, where $c_1,c_2$ are absolute constants. In this paper, following these results, we prove that, there exists a set A of integers such that: $r_A(n)=1$ for all integers n and $d_A(n)=1$ for all positive integers n, $|S(x)bigcup S(y)|leqslant 4|S(x+y)|$ for $x,yin A$ and $A(-x,x) gt (4/log 5)loglog x+c$ for all $xgeqslant 1$, where c is an absolute constant. Furthermore, we also construct a family of arbitrarily spare such sets A.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42559236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

New mock theta functions and formulas for basic hypergeometric series 新的模拟函数和基本超几何级数的公式

IF 0.7 3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-08-01 DOI: 10.1017/S0013091523000457

Olivia X. M. Yao

引用次数: 0

The spectral eigenmatrix problems of planar self-affine measures with four digits 平面四位数自仿射测度的谱特征矩阵问题

IF 0.7 3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-08-01 DOI: 10.1017/S0013091523000469

Jingcheng Liu, Min-Wei Tang, Shan Wu

引用次数: 1

Corrigendum: Von Neumann Algebras and Extensions of Inverse Semigroups 勘误:Von Neumann代数和逆半群的扩展

3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-08-01 DOI: 10.1017/s0013091523000470

Allan P. Donsig, Adam H. Fuller, David R. Pitts

引用次数: 0

PEM series 2 volume 66 issue 3 Cover and Front matter PEM系列2第66卷第3期封面和封面

IF 0.7 3区数学

Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-08-01 DOI: 10.1017/s0013091523000512

引用次数: 0