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Weighted holomorphic Dirichlet series and composition operators with polynomial symbols 加权全纯Dirichlet级数与多项式符号的复合算子
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-04-14 DOI: 10.7146/math.scand.a-129686
E. Fricain, Camille Mau
{"title":"Weighted holomorphic Dirichlet series and composition operators with polynomial symbols","authors":"E. Fricain, Camille Mau","doi":"10.7146/math.scand.a-129686","DOIUrl":"https://doi.org/10.7146/math.scand.a-129686","url":null,"abstract":"In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol inducing the composition operator is an affine function, we give criteria for boundedness and compactness. We also study the cyclicity property and as a byproduct give a characterization so that the direct sum of the identity plus a weighted forward shift operator on $ell^2$ is cyclic.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42238536","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
Volume title pages 卷标题页
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-02-17 DOI: 10.7146/MATH.SCAND.A-125054
Mathematica Scandinavica
{"title":"Volume title pages","authors":"Mathematica Scandinavica","doi":"10.7146/MATH.SCAND.A-125054","DOIUrl":"https://doi.org/10.7146/MATH.SCAND.A-125054","url":null,"abstract":"Volume title pages","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71076820","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
Affine and formal abelian group schemes on $p$-polar rings $p$-极环上的仿射和形式阿贝尔群方案
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2020-12-18 DOI: 10.7146/math.scand.a-129704
Tilman Bauer
{"title":"Affine and formal abelian group schemes on $p$-polar rings","authors":"Tilman Bauer","doi":"10.7146/math.scand.a-129704","DOIUrl":"https://doi.org/10.7146/math.scand.a-129704","url":null,"abstract":"We show that the functor of $p$-typical co-Witt vectors on commutative algebras over a perfect field $k$ of characteristic $p$ is defined on, and in fact only depends on, a weaker structure than that of a $k$-algebra. We call this structure a $p$-polar $k$-algebra. By extension, the functors of points for any $p$-adic affine commutative group scheme and for any formal group are defined on, and only depend on, $p$-polar structures. In terms of abelian Hopf algebras, we show that a cofree cocommutative Hopf algebra can be defined on any $p$-polar $k$-algebra $P$, and it agrees with the cofree commutative Hopf algebra on a commutative $k$-algebra $A$ if $P$ is the $p$-polar algebra underlying $A$; a dual result holds for free commutative Hopf algebras on finite $k$-coalgebras.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47582937","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: 3
$lambda$-quiddité sur $mathbb{Z}[alpha]$ avec $alpha$ transcendant $lambda$-在$mathbb{Z}[alpha]$上具有$alpha$超越
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2020-11-13 DOI: 10.7146/math.scand.a-128972
Flavien Mabilat
{"title":"$lambda$-quiddité sur $mathbb{Z}[alpha]$ avec $alpha$ transcendant","authors":"Flavien Mabilat","doi":"10.7146/math.scand.a-128972","DOIUrl":"https://doi.org/10.7146/math.scand.a-128972","url":null,"abstract":"Dans le cadre de l'étude des frises de Coxeter, M. Cuntz a introduit la notion de $lambda$-quiddité irréductible. L'objectif de cette note est de lister toutes les $lambda$-quiddités irréductibles sur l'anneau $mathbb{Z}[alpha]$ dans le cas où $alpha$ est un nombre complexe transcendant.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43754279","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
Density of $f$-ideals and $f$-ideals in mixed small degrees 混合小度中$f$-理想和$f$–理想的密度
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2020-11-05 DOI: 10.7146/math.scand.a-129244
HÀ Huytài, Graham Keiper, H. Mahmood, Jonathan L. O'Rourke
{"title":"Density of $f$-ideals and $f$-ideals in mixed small degrees","authors":"HÀ Huytài, Graham Keiper, H. Mahmood, Jonathan L. O'Rourke","doi":"10.7146/math.scand.a-129244","DOIUrl":"https://doi.org/10.7146/math.scand.a-129244","url":null,"abstract":"A squarefree monomial ideal is called an $f$-ideal if its Stanley–Reisner and facet simplicial complexes have the same $f$-vector. We show that $f$-ideals generated in a fixed degree have asymptotic density zero when the number of variables goes to infinity. We also provide novel algorithms to construct $f$-ideals generated in small degrees.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44515481","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
Dimension of images of large level sets 大型水平集图像的尺寸
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2020-10-22 DOI: 10.7146/math.scand.a-129246
A. O’Farrell, G. Armstrong
{"title":"Dimension of images of large level sets","authors":"A. O’Farrell, G. Armstrong","doi":"10.7146/math.scand.a-129246","DOIUrl":"https://doi.org/10.7146/math.scand.a-129246","url":null,"abstract":"Let $k$ be a natural number. We consider $k$-times continuously differentiable real-valued functions $fcolon Eto mathbb{R} $, where $E$ is some interval on the line having positive length. For $0<alpha <1$ let $I_alpha (f)$ denote the set of values $yin mathbb{R} $ whose preimage $f^{-1}(y)$ has Hausdorff dimension at least $alpha$. We consider how large can be the Hausdorff dimension of $I_alpha (f)$, as $f$ ranges over the set of all $k$-times continuously differentiable functions from $E$ into $mathbb{R} $. We show that the sharp upper bound on $dim I_alpha (f)$ is $(1-alpha )/k$.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42351127","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
Componentwise linear powers and the $x$-condition 分量线性幂和x条件
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2020-10-22 DOI: 10.7146/math.scand.a-133265
J. Herzog, T. Hibi, S. Moradi
{"title":"Componentwise linear powers and the $x$-condition","authors":"J. Herzog, T. Hibi, S. Moradi","doi":"10.7146/math.scand.a-133265","DOIUrl":"https://doi.org/10.7146/math.scand.a-133265","url":null,"abstract":"Let $S=K[x_1,ldots,x_n]$ be the polynomial ring over a field and $A$ a standard graded $S$-algebra. In terms of the Gröbner basis of the defining ideal $J$ of $A$ we give a condition, called the $x$-condition, which implies that all graded components $A_k$ of $A$ have linear quotients and with additional assumptions are componentwise linear. A typical example of such an algebra is the Rees ring $mathcal{R}(I)$ of a graded ideal or the symmetric algebra $textrm{Sym}(M)$ of a module $M$. We apply our criterion to study certain symmetric algebras and the powers of vertex cover ideals of certain classes of graphs.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43122853","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
Fredholm theory of Toeplitz operators on doubling Fock Hilbert spaces 复倍Fock Hilbert空间上Toeplitz算子的Fredholm理论
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2020-09-03 DOI: 10.7146/MATH.SCAND.A-120920
Aamena Al-Qabani, T. Hilberdink, J. Virtanen
{"title":"Fredholm theory of Toeplitz operators on doubling Fock Hilbert spaces","authors":"Aamena Al-Qabani, T. Hilberdink, J. Virtanen","doi":"10.7146/MATH.SCAND.A-120920","DOIUrl":"https://doi.org/10.7146/MATH.SCAND.A-120920","url":null,"abstract":"We study the Fredholm properties of Toeplitz operators acting on doubling Fock Hilbert spaces, and describe their essential spectra for bounded symbols of vanishing oscillation. We also compute the index of these Toeplitz operators in the special case when $varphi (z) = lvert {z}rvert^{beta }$ with $beta >0$. Our work extends the recent results on Toeplitz operators on the standard weighted Fock spaces to the setting of doubling Fock spaces.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47032503","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: 3
Weighted composition operators on weighted Bergman spaces induced by doubling weights 权重加倍诱导的加权Bergman空间上的加权复合算子
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2020-09-03 DOI: 10.7146/math.scand.a-119741
Juntao Du, Songxiao Li, Yecheng Shi
{"title":"Weighted composition operators on weighted Bergman spaces induced by doubling weights","authors":"Juntao Du, Songxiao Li, Yecheng Shi","doi":"10.7146/math.scand.a-119741","DOIUrl":"https://doi.org/10.7146/math.scand.a-119741","url":null,"abstract":"In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators uCφ on Bergman type spaces Apω induced by a doubling weight ω. Let X={u∈H(D):uCφ:Apω→Apω is bounded}. For some regular weights ω, we obtain that X=H∞ if and only if ϕ is a finite Blaschke product.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42079876","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: 3
The block Schur product is a Hadamard product 块舒尔产品是阿达玛产品
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2020-09-03 DOI: 10.7146/math.scand.a-121069
Erik Christensen
{"title":"The block Schur product is a Hadamard product","authors":"Erik Christensen","doi":"10.7146/math.scand.a-121069","DOIUrl":"https://doi.org/10.7146/math.scand.a-121069","url":null,"abstract":"Given two $n times n $ matrices $A = (a_{ij})$ and $B=(b_{ij}) $ with entries in $B(H)$ for some Hilbert space $H$, their block Schur product is the $n times n$ matrix $ Asquare B := (a_{ij}b_{ij})$. Given two continuous functions $f$ and $g$ on the torus with Fourier coefficients $(f_n)$ and $(g_n)$ their convolution product $f star g$ has Fourier coefficients $(f_n g_n)$. Based on this, the Schur product on scalar matrices is also known as the Hadamard product. \u0000We show that for a C*-algebra $mathcal{A} $, and a discrete group $G$ with an action $alpha _g$ of $G$ on $mathcal{A} $ by *-automorphisms, the reduced crossed product C*-algebra $mathrm {C}^*_r(mathcal{A} , alpha , G)$ possesses a natural generalization of the convolution product, which we suggest should be named the Hadamard product. \u0000We show that this product has a natural Stinespring representation and we lift some known results on block Schur products to this setting, but we also show that the block Schur product is a special case of the Hadamard product in a crossed product algebra.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46242078","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: 2
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