Pub Date : 2023-04-10DOI: 10.4153/s0008439523000693
Chris Bruce, Eduardo Scarparo
We investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers $p$ and $q$, we show that Furstenberg's $times p,times q$ conjecture holds if and only if the canonical trace is the only faithful extreme tracial state on the $C^*$-algebra of the group $mathbb{Z}[frac{1}{pq}]rtimesmathbb{Z}^2$. We also compute the primitive ideal space and K-theory of $C^*(mathbb{Z}[frac{1}{pq}]rtimesmathbb{Z}^2)$.
{"title":"A TRACIAL CHARACTERIZATION OF FURSTENBERG’S CONJECTURE","authors":"Chris Bruce, Eduardo Scarparo","doi":"10.4153/s0008439523000693","DOIUrl":"https://doi.org/10.4153/s0008439523000693","url":null,"abstract":"We investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers $p$ and $q$, we show that Furstenberg's $times p,times q$ conjecture holds if and only if the canonical trace is the only faithful extreme tracial state on the $C^*$-algebra of the group $mathbb{Z}[frac{1}{pq}]rtimesmathbb{Z}^2$. We also compute the primitive ideal space and K-theory of $C^*(mathbb{Z}[frac{1}{pq}]rtimesmathbb{Z}^2)$.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46704468","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}
Pub Date : 2023-03-29DOI: 10.4153/s0008439523000231
Daniel Cavey
{"title":"A note on the smooth blow-ups of in torus-invariant subvarieties","authors":"Daniel Cavey","doi":"10.4153/s0008439523000231","DOIUrl":"https://doi.org/10.4153/s0008439523000231","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48750162","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}
Pub Date : 2023-03-22DOI: 10.4153/s000843952300022x
Martin Čech
{"title":"Mean value of real Dirichlet characters using a double Dirichlet series","authors":"Martin Čech","doi":"10.4153/s000843952300022x","DOIUrl":"https://doi.org/10.4153/s000843952300022x","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45538207","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}
Pub Date : 2023-02-28DOI: 10.4153/s0008439523000188
E. SHCHEPIN, V. VALOV
Abstract We discuss the question of extending homeomorphisms between closed subsets of the Cantor cube $D^{tau }$ . It is established that any homeomorphism between two closed negligible subsets of $D^{tau }$ can be extended to an autohomeomorphism of $D^{tau }$ .
{"title":"On homogeneity of Cantor cubes","authors":"E. SHCHEPIN, V. VALOV","doi":"10.4153/s0008439523000188","DOIUrl":"https://doi.org/10.4153/s0008439523000188","url":null,"abstract":"Abstract We discuss the question of extending homeomorphisms between closed subsets of the Cantor cube $D^{tau }$ . It is established that any homeomorphism between two closed negligible subsets of $D^{tau }$ can be extended to an autohomeomorphism of $D^{tau }$ .","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135583087","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}
Pub Date : 2023-02-27DOI: 10.4153/s000843952300053x
S. Shaabani
We prove that the Hardy-Littlewood maximal operator is discontinuous on $bmorn$ and maps $vmorn$ to itself. A counterexample to boundedness of the strong and directional maximal operators on $bmorn$ is given, and properties of slices of $bmorn$ functions are discussed.
{"title":"MAXIMAL OPERATORS ON BMO AND SLICES","authors":"S. Shaabani","doi":"10.4153/s000843952300053x","DOIUrl":"https://doi.org/10.4153/s000843952300053x","url":null,"abstract":"We prove that the Hardy-Littlewood maximal operator is discontinuous on $bmorn$ and maps $vmorn$ to itself. A counterexample to boundedness of the strong and directional maximal operators on $bmorn$ is given, and properties of slices of $bmorn$ functions are discussed.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49239679","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}
Pub Date : 2023-02-21DOI: 10.4153/s0008439523000176
P. Casazza, S. Dilworth, D. Kutzarova, P. Motakis
{"title":"New characterizations of the unit vector basis of or","authors":"P. Casazza, S. Dilworth, D. Kutzarova, P. Motakis","doi":"10.4153/s0008439523000176","DOIUrl":"https://doi.org/10.4153/s0008439523000176","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43034671","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}
Pub Date : 2023-02-17DOI: 10.4153/S0008439523000164
Nicolae Strungaru
Abstract In this paper, we prove that given a cut-and-project scheme $(G, H, mathcal {L})$ and a compact window $W subseteq H$ , the natural projection gives a bijection between the Fourier transformable measures on $G times H$ supported inside the strip ${mathcal L} cap (G times W)$ and the Fourier transformable measures on G supported inside ${LARGE curlywedge }(W)$ . We provide a closed formula relating the Fourier transform of the original measure and the Fourier transform of the projection. We show that this formula can be used to re-derive some known results about Fourier analysis of measures with weak Meyer set support.
摘要本文证明了给定一个切投影方案$(G, H， mathcal {L})$和一个紧窗$W 子集$ H$，其自然投影给出了支持在条形${mathcal L} cap (G times W)$内的$G × H$上的傅里叶变换测度与支持在${LARGE curlywedge}(W)$内的G上的傅里叶变换测度之间的双射。我们提供了一个关于原始测度的傅里叶变换和投影的傅里叶变换的封闭公式。我们证明了这个公式可以用来重新推导一些已知的关于弱Meyer集支持测度的傅里叶分析的结果。
{"title":"Fourier transformable measures with weak Meyer set support and their lift to the cut-and-project scheme","authors":"Nicolae Strungaru","doi":"10.4153/S0008439523000164","DOIUrl":"https://doi.org/10.4153/S0008439523000164","url":null,"abstract":"Abstract In this paper, we prove that given a cut-and-project scheme \u0000$(G, H, mathcal {L})$\u0000 and a compact window \u0000$W subseteq H$\u0000 , the natural projection gives a bijection between the Fourier transformable measures on \u0000$G times H$\u0000 supported inside the strip \u0000${mathcal L} cap (G times W)$\u0000 and the Fourier transformable measures on G supported inside \u0000${LARGE curlywedge }(W)$\u0000 . We provide a closed formula relating the Fourier transform of the original measure and the Fourier transform of the projection. We show that this formula can be used to re-derive some known results about Fourier analysis of measures with weak Meyer set support.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":"66 1","pages":"1044 - 1060"},"PeriodicalIF":0.6,"publicationDate":"2023-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43774674","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}
Pub Date : 2023-02-15DOI: 10.4153/s0008439523000577
Ming-Sheng Liu, S. Ponnusamy
In this paper, we establish three new versions of Landau-type theorems for bounded bi-analytic functions of the form $F(z)=bar{z}G(z)+H(z)$, where $G$ and $H$ are analytic in the unit disk $|z|<1$ with $G(0)=H(0)=0$ and $H'(0)=1$. In particular, two of them are sharp while the other one either generalizes or improves the corresponding result of Abdulhadi and Hajj. As consequences, several new sharp versions of Landau-type theorems for certain subclasses of bounded biharmonic mappings are proved.
{"title":"LANDAU-TYPE THEOREMS FOR CERTAIN BOUNDED BI-ANALYTIC FUNCTIONS AND BIHARMONIC MAPPINGS","authors":"Ming-Sheng Liu, S. Ponnusamy","doi":"10.4153/s0008439523000577","DOIUrl":"https://doi.org/10.4153/s0008439523000577","url":null,"abstract":"In this paper, we establish three new versions of Landau-type theorems for bounded bi-analytic functions of the form $F(z)=bar{z}G(z)+H(z)$, where $G$ and $H$ are analytic in the unit disk $|z|<1$ with $G(0)=H(0)=0$ and $H'(0)=1$. In particular, two of them are sharp while the other one either generalizes or improves the corresponding result of Abdulhadi and Hajj. As consequences, several new sharp versions of Landau-type theorems for certain subclasses of bounded biharmonic mappings are proved.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46810851","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}
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