Pub Date : 2023-03-20DOI: 10.4153/s0008414x23000135
Robert McCann, K. Bringmann, P. Bravi, J. Gandini, M. A. H. Cifre, Miriam Tárraga, Osvaldo Guzmán, Jonah Gaster, Brice Loustau
{"title":"CJM volume 75 issue 2 Cover and Front matter","authors":"Robert McCann, K. Bringmann, P. Bravi, J. Gandini, M. A. H. Cifre, Miriam Tárraga, Osvaldo Guzmán, Jonah Gaster, Brice Loustau","doi":"10.4153/s0008414x23000135","DOIUrl":"https://doi.org/10.4153/s0008414x23000135","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"133 1","pages":"f1 - f3"},"PeriodicalIF":0.7,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79384140","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}
Pub Date : 2023-03-03DOI: 10.4153/s0008414x23000123
J. Andrade, S. Boatto, F. Crespo, D. Espejo
{"title":"On the stability of ring relative equilibria in the -body problem on with Hodge potential","authors":"J. Andrade, S. Boatto, F. Crespo, D. Espejo","doi":"10.4153/s0008414x23000123","DOIUrl":"https://doi.org/10.4153/s0008414x23000123","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"3 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89701954","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}
Pub Date : 2023-02-03DOI: 10.4153/s0008414x23000494
S. Luo, Kehe Zhu
For a bounded analytic function $varphi$ on the unit disk $D$ with $|varphi|_inftyle1$ we consider the defect operators $D_varphi$ and $D_{overlinevarphi}$ of the Toeplitz operators $T_varphi$ and $T_{overlinevarphi}$, respectively, on the weighted Bergman space $A^2_alpha$. The ranges of $D_varphi$ and $D_{overlinevarphi}$, written as $H(varphi)$ and $H(overlinevarphi)$ and equipped with appropriate inner products, are called sub-Bergman spaces. We prove the following three results in the paper: for $-1-1$ we have $H(varphi)=H(overlinevarphi)=A^2_{alpha-1}$ if and only if the defect operators $D_varphi$ and $D_{overlinevarphi}$ are compact; and for $alpha>-1$ we have $D^2_varphi(A^2_alpha)= D^2_{overlinevarphi}(A^2_alpha)=A^2_{alpha-2}$ if and only if $varphi$ is a finite Blaschke product. In some sense our restrictions on $alpha$ here are best possible.
{"title":"Sub-Bergman Hilbert spaces on the unit disk III","authors":"S. Luo, Kehe Zhu","doi":"10.4153/s0008414x23000494","DOIUrl":"https://doi.org/10.4153/s0008414x23000494","url":null,"abstract":"For a bounded analytic function $varphi$ on the unit disk $D$ with $|varphi|_inftyle1$ we consider the defect operators $D_varphi$ and $D_{overlinevarphi}$ of the Toeplitz operators $T_varphi$ and $T_{overlinevarphi}$, respectively, on the weighted Bergman space $A^2_alpha$. The ranges of $D_varphi$ and $D_{overlinevarphi}$, written as $H(varphi)$ and $H(overlinevarphi)$ and equipped with appropriate inner products, are called sub-Bergman spaces. We prove the following three results in the paper: for $-1<alphale0$ the space $H(varphi)$ has a complete Nevanlinna-Pick kernel if and only if $varphi$ is a M\"{o}bius map; for $alpha>-1$ we have $H(varphi)=H(overlinevarphi)=A^2_{alpha-1}$ if and only if the defect operators $D_varphi$ and $D_{overlinevarphi}$ are compact; and for $alpha>-1$ we have $D^2_varphi(A^2_alpha)= D^2_{overlinevarphi}(A^2_alpha)=A^2_{alpha-2}$ if and only if $varphi$ is a finite Blaschke product. In some sense our restrictions on $alpha$ here are best possible.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"34 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79995372","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}
Pub Date : 2023-02-01DOI: 10.4153/s0008414x23000020
{"title":"CJM volume 75 issue 1 Cover and Front matter","authors":"","doi":"10.4153/s0008414x23000020","DOIUrl":"https://doi.org/10.4153/s0008414x23000020","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"26 1","pages":"f1 - f3"},"PeriodicalIF":0.7,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74782818","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}
Pub Date : 2023-02-01DOI: 10.4153/s0008414x23000032
{"title":"CJM volume 75 issue 1 Cover and Back matter","authors":"","doi":"10.4153/s0008414x23000032","DOIUrl":"https://doi.org/10.4153/s0008414x23000032","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"35 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86682706","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}
Pub Date : 2023-01-22DOI: 10.4153/s0008414x23000500
I. Shkredov
In our paper we study multiplicative properties of difference sets $A-A$ for large sets $A subseteq mathbb{Z}/qmathbb{Z}$ in the case of composite $q$. We obtain a quantitative version of a result of A. Fish about the structure of the product sets $(A-A)(A-A)$. Also, we show that the multiplicative covering number of any difference set is always small.
在合数$q$的情况下，研究了大集合$A subseteq mathbb{Z}/qmathbb{Z}$的差分集$A-A$的乘法性质。我们得到了a . Fish关于积集$(a - a)$ (a - a)$结构的结果的一个定量版本。并且证明了任意差分集的乘法覆盖数总是很小的。
{"title":"On some multiplicative properties of large difference sets","authors":"I. Shkredov","doi":"10.4153/s0008414x23000500","DOIUrl":"https://doi.org/10.4153/s0008414x23000500","url":null,"abstract":"In our paper we study multiplicative properties of difference sets $A-A$ for large sets $A subseteq mathbb{Z}/qmathbb{Z}$ in the case of composite $q$. We obtain a quantitative version of a result of A. Fish about the structure of the product sets $(A-A)(A-A)$. Also, we show that the multiplicative covering number of any difference set is always small.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72890357","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}
Pub Date : 2023-01-06DOI: 10.4153/s0008414x2300041x
Guy Boyde, R. Huang
Inspired by a remarkable work of F'{e}lix, Halperin and Thomas on the asymptotic estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors on local hyperbolicity, we prove two asymptotic formulae for torsion rank of homotopy groups, one using ordinary homology and one using $K$-theory. We use these to obtain explicit quantitative asymptotic lower bounds on the torsion rank of the homotopy groups for many interesting spaces after suspension, including Moore spaces, Eilenberg-MacLane spaces, complex projective spaces, complex Grassmannians, Milnor hypersurfaces and unitary groups.
{"title":"Some asymptotic formulae for torsion in homotopy groups","authors":"Guy Boyde, R. Huang","doi":"10.4153/s0008414x2300041x","DOIUrl":"https://doi.org/10.4153/s0008414x2300041x","url":null,"abstract":"Inspired by a remarkable work of F'{e}lix, Halperin and Thomas on the asymptotic estimation of the ranks of rational homotopy groups, and more recent works of Wu and the authors on local hyperbolicity, we prove two asymptotic formulae for torsion rank of homotopy groups, one using ordinary homology and one using $K$-theory. We use these to obtain explicit quantitative asymptotic lower bounds on the torsion rank of the homotopy groups for many interesting spaces after suspension, including Moore spaces, Eilenberg-MacLane spaces, complex projective spaces, complex Grassmannians, Milnor hypersurfaces and unitary groups.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"31 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85640439","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}
Pub Date : 2022-12-01DOI: 10.4153/s0008414x22000463
Robert McCann, K. Bringmann, H. Maldeghem, K. Ebrahimi-Fard, F. Patras, N. Tapia
{"title":"CJM volume 74 issue 6 Cover and Front matter","authors":"Robert McCann, K. Bringmann, H. Maldeghem, K. Ebrahimi-Fard, F. Patras, N. Tapia","doi":"10.4153/s0008414x22000463","DOIUrl":"https://doi.org/10.4153/s0008414x22000463","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"8 1","pages":"f1 - f3"},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90132974","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}
Pub Date : 2022-12-01DOI: 10.4153/s0008414x22000475
{"title":"CJM volume 74 issue 6 Cover and Back matter","authors":"","doi":"10.4153/s0008414x22000475","DOIUrl":"https://doi.org/10.4153/s0008414x22000475","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"30 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81388857","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}
Pub Date : 2022-11-21DOI: 10.4153/s0008414x22000621
K. Ihara, Y. Kusunoki, Yayoi Nakamura, Hitomi Saeki
{"title":"Generating function of multiple polylog of Hurwitz type","authors":"K. Ihara, Y. Kusunoki, Yayoi Nakamura, Hitomi Saeki","doi":"10.4153/s0008414x22000621","DOIUrl":"https://doi.org/10.4153/s0008414x22000621","url":null,"abstract":"","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"60 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72528380","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}
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