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LINEAR PRESERVERS ON IDEMPOTENTS OF FOURIER ALGEBRAS 傅立叶代数幂等元的线性保持器
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-02-02 DOI: 10.4153/s0008439523000395
Ying-Fen Lin, Shiho Oi
{"title":"LINEAR PRESERVERS ON IDEMPOTENTS OF FOURIER ALGEBRAS","authors":"Ying-Fen Lin, Shiho Oi","doi":"10.4153/s0008439523000395","DOIUrl":"https://doi.org/10.4153/s0008439523000395","url":null,"abstract":"In this article, we give a representation of bounded complex linear operators which preserve idempotent elements on the Fourier algebra of a locally compact group. When such an operator is moreover positive or contractive, we show that the operator is induced by either a continuous group homomorphism or a continuous group anti-homomorphism. If the groups are totally disconnected, bounded homomorphisms on the Fourier algebra can be realised by the idempotent preserving operators.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47254819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Erdős–Ko–Rado theorem in Peisert-type graphs Peisert型图中的Erdõs–Ko–Rado定理
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-02-01 DOI: 10.4153/S0008439523000607
Chi Hoi Yip
{"title":"Erdős–Ko–Rado theorem in Peisert-type graphs","authors":"Chi Hoi Yip","doi":"10.4153/S0008439523000607","DOIUrl":"https://doi.org/10.4153/S0008439523000607","url":null,"abstract":"The celebrated ErdH{o}s-Ko-Rado (EKR) theorem for Paley graphs (of square order) states that all maximum cliques are canonical in the sense that each maximum clique arises from the subfield construction. Recently, Asgarli and Yip extended this result to Peisert graphs and other Cayley graphs which are Peisert-type graphs with nice algebraic properties on the connection set. On the other hand, there are Peisert-type graphs for which the EKR theorem fails to hold. In this paper, we show that the EKR theorem of Paley graphs extends to almost all pseudo-Paley graphs of Peisert-type. Furthermore, we establish the stability results of the same flavor.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41959603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Bohr–Rogosinski radius for a certain class of close-to-convex harmonic mappings 一类近凸调和映射的Bohr-Rogosinski半径
4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-01-31 DOI: 10.4153/s0008439523000115
MOLLA BASIR AHAMED, VASUDEVARAO ALLU
{"title":"Bohr–Rogosinski radius for a certain class of close-to-convex harmonic mappings","authors":"MOLLA BASIR AHAMED, VASUDEVARAO ALLU","doi":"10.4153/s0008439523000115","DOIUrl":"https://doi.org/10.4153/s0008439523000115","url":null,"abstract":"Abstract Let \u0000$ mathcal {B} $\u0000 be the class of analytic functions \u0000$ f $\u0000 in the unit disk \u0000$ mathbb {D}={zin mathbb {C} : |z|<1} $\u0000 such that \u0000$ |f(z)|<1 $\u0000 for all \u0000$ zin mathbb {D} $\u0000 . If \u0000$ fin mathcal {B} $\u0000 of the form \u0000$ f(z)=sum _{n=0}^{infty }a_nz^n $\u0000 , then \u0000$ sum _{n=0}^{infty }|a_nz^n|leq 1 $\u0000 for \u0000$ |z|=rleq 1/3 $\u0000 and \u0000$ 1/3 $\u0000 cannot be improved. This inequality is called Bohr inequality and the quantity \u0000$ 1/3 $\u0000 is called Bohr radius. If \u0000$ fin mathcal {B} $\u0000 of the form \u0000$ f(z)=sum _{n=0}^{infty }a_nz^n $\u0000 , then \u0000$ |sum _{n=0}^{N}a_nz^n|<1;; mbox {for};; |z|<{1}/{2} $\u0000 and the radius \u0000$ 1/2 $\u0000 is the best possible for the class \u0000$ mathcal {B} $\u0000 . This inequality is called Bohr–Rogosinski inequality and the corresponding radius is called Bohr–Rogosinski radius. Let \u0000$ mathcal {H} $\u0000 be the class of all complex-valued harmonic functions \u0000$ f=h+bar {g} $\u0000 defined on the unit disk \u0000$ mathbb {D} $\u0000 , where \u0000$ h $\u0000 and \u0000$ g $\u0000 are analytic in \u0000$ mathbb {D} $\u0000 with the normalization \u0000$ h(0)=h^{prime }(0)-1=0 $\u0000 and \u0000$ g(0)=0 $\u0000 . Let \u0000$ mathcal {H}_0={f=h+bar {g}in mathcal {H} : g^{prime }(0)=0}. $\u0000 For \u0000$ alpha geq 0 $\u0000 and \u0000$ 0leq beta <1 $\u0000 , let \u0000$$ begin{align*} mathcal{W}^{0}_{mathcal{H}}(alpha, beta)={f=h+overline{g}inmathcal{H}_{0} : mathrm{Re}left(h^{prime}(z)+alpha zh^{primeprime}(z)-betaright)>|g^{prime}(z)+alpha zg^{primeprime}(z)|,;; zinmathbb{D}} end{align*} $$\u0000 be a class of close-to-convex harmonic mappings in \u0000$ mathbb {D} $\u0000 . In this paper, we prove the sharp Bohr–Rogosinski radius for the class \u0000$ mathcal {W}^{0}_{mathcal {H}}(alpha , beta ) $\u0000 .","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135306205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Invariant means on weakly almost periodic functionals with application to quantum groups 弱概周期泛函的不变量意义及其在量子群上的应用
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-01-16 DOI: 10.4153/S0008439523000061
Ali Ebrahimzadeh Esfahani, M. Nemati, Mohammad Reza Ghanei
{"title":"Invariant means on weakly almost periodic functionals with application to quantum groups","authors":"Ali Ebrahimzadeh Esfahani, M. Nemati, Mohammad Reza Ghanei","doi":"10.4153/S0008439523000061","DOIUrl":"https://doi.org/10.4153/S0008439523000061","url":null,"abstract":"Abstract Let \u0000${mathcal A}$\u0000 be a Banach algebra, and let \u0000$varphi $\u0000 be a nonzero character on \u0000${mathcal A}$\u0000 . For a closed ideal I of \u0000${mathcal A}$\u0000 with \u0000$Inot subseteq ker varphi $\u0000 such that I has a bounded approximate identity, we show that \u0000$operatorname {WAP}(mathcal {A})$\u0000 , the space of weakly almost periodic functionals on \u0000${mathcal A}$\u0000 , admits a right (left) invariant \u0000$varphi $\u0000 -mean if and only if \u0000$operatorname {WAP}(I)$\u0000 admits a right (left) invariant \u0000$varphi |_I$\u0000 -mean. This generalizes a result due to Neufang for the group algebra \u0000$L^1(G)$\u0000 as an ideal in the measure algebra \u0000$M(G)$\u0000 , for a locally compact group G. Then we apply this result to the quantum group algebra \u0000$L^1({mathbb G})$\u0000 of a locally compact quantum group \u0000${mathbb G}$\u0000 . Finally, we study the existence of left and right invariant \u0000$1$\u0000 -means on \u0000$ operatorname {WAP}(mathcal {T}_{triangleright }({mathbb G}))$\u0000 .","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44999520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 note on cyclic vectors in Dirichlet-type spaces in the unit ball of ${mathbb C}^n$ 单位球${mathbb C}^n$中dirichlet型空间中循环向量的注释
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-01-13 DOI: 10.4153/S0008439523000085
Dimitrios Vavitsas
{"title":"A note on cyclic vectors in Dirichlet-type spaces in the unit ball of \u0000${mathbb C}^n$","authors":"Dimitrios Vavitsas","doi":"10.4153/S0008439523000085","DOIUrl":"https://doi.org/10.4153/S0008439523000085","url":null,"abstract":"Abstract We characterize model polynomials that are cyclic in Dirichlet-type spaces in the unit ball of \u0000$mathbb C^n$\u0000 , and we give a sufficient capacity condition in order to identify noncyclic vectors.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46821753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Invariant ideals and their applications to the turnpike theory 不变理想及其在收费公路理论中的应用
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-01-12 DOI: 10.4153/S0008439523000036
Musa Mammadov, Piotr Szuca
{"title":"Invariant ideals and their applications to the turnpike theory","authors":"Musa Mammadov, Piotr Szuca","doi":"10.4153/S0008439523000036","DOIUrl":"https://doi.org/10.4153/S0008439523000036","url":null,"abstract":"Abstract In this paper, the turnpike property is established for a nonconvex optimal control problem in discrete time. The functional is defined by the notion of the ideal convergence and can be considered as an analogue of the terminal functional defined over infinite-time horizon. The turnpike property states that every optimal solution converges to some unique optimal stationary point in the sense of ideal convergence if the ideal is invariant under translations. This kind of convergence generalizes, for example, statistical convergence and convergence with respect to logarithmic density zero sets.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46038387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Mahler measure of polynomial iterates 多项式的马勒测度迭代
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-01-12 DOI: 10.4153/S0008439523000048
I. Pritsker
{"title":"Mahler measure of polynomial iterates","authors":"I. Pritsker","doi":"10.4153/S0008439523000048","DOIUrl":"https://doi.org/10.4153/S0008439523000048","url":null,"abstract":"Abstract Granville recently asked how the Mahler measure behaves in the context of polynomial dynamics. For a polynomial \u0000$f(z)=z^d+cdots in {mathbb C}[z], deg (f)ge 2,$\u0000 we show that the Mahler measure of the iterates \u0000$f^n$\u0000 grows geometrically fast with the degree \u0000$d^n,$\u0000 and find the exact base of that exponential growth. This base is expressed via an integral of \u0000$log ^+|z|$\u0000 with respect to the invariant measure of the Julia set for the polynomial \u0000$f.$\u0000 Moreover, we give sharp estimates for such an integral when the Julia set is connected.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41334980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Irrational braided generalized near-groups 非理性辫状广义近群
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-12-28 DOI: 10.4153/s0008439523000334
Andrew Schopieray
{"title":"Irrational braided generalized near-groups","authors":"Andrew Schopieray","doi":"10.4153/s0008439523000334","DOIUrl":"https://doi.org/10.4153/s0008439523000334","url":null,"abstract":"We classify braided generalized near-group fusion categories whose global dimension is not an integer; there are exactly two up to Grothendieck equivalence and taking products with braided pointed fusion categories.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48547669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Square roots of weighted shifts of multiplicity two 重数2的加权移位的平方根
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-12-23 DOI: 10.4153/S000843952200073X
Chanaka Kottegoda, Trieu Le, Tomas Miguel Rodriguez
{"title":"Square roots of weighted shifts of multiplicity two","authors":"Chanaka Kottegoda, Trieu Le, Tomas Miguel Rodriguez","doi":"10.4153/S000843952200073X","DOIUrl":"https://doi.org/10.4153/S000843952200073X","url":null,"abstract":"Abstract Given a weighted shift T of multiplicity two, we study the set \u0000$sqrt {T}$\u0000 of all square roots of T. We determine necessary and sufficient conditions on the weight sequence so that this set is non-empty. We show that when such conditions are satisfied, \u0000$sqrt {T}$\u0000 contains a certain special class of operators. We also obtain a complete description of all operators in \u0000$sqrt {T}$\u0000 .","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49497365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Smooth numbers with few non-zero binary digits 具有少量非零二进制数的光滑数
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-12-20 DOI: 10.4153/s0008439523000504
Maximilian Hauck, I. Shparlinski
{"title":"Smooth numbers with few non-zero binary digits","authors":"Maximilian Hauck, I. Shparlinski","doi":"10.4153/s0008439523000504","DOIUrl":"https://doi.org/10.4153/s0008439523000504","url":null,"abstract":"We use bounds of character sums and some combinatorial arguments to show the abundance of very smooth numbers which also have very few non-zero binary digits.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48991747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
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