Pub Date : 2020-09-03DOI: 10.7146/math.scand.a-121167
Ewa Kozłowska-Walania
We study the symmetric Riemann surfaces for which the group of orientation preserving automorphisms acts without fixed points. We show that any finite group can give rise to such an action, determine the maximal number of non-conjugate symmetries for such surfaces and find a sharp upper bound on maximal total number of ovals for a set of k symmetries with ovals. We also solve the minimal genus problem for dihedral groups acting on the surfaces described above, for odd genera.
{"title":"Symmetric Riemann surfaces with no points fixed by orientation preserving automorphisms","authors":"Ewa Kozłowska-Walania","doi":"10.7146/math.scand.a-121167","DOIUrl":"https://doi.org/10.7146/math.scand.a-121167","url":null,"abstract":"We study the symmetric Riemann surfaces for which the group of orientation preserving automorphisms acts without fixed points. We show that any finite group can give rise to such an action, determine the maximal number of non-conjugate symmetries for such surfaces and find a sharp upper bound on maximal total number of ovals for a set of k symmetries with ovals. We also solve the minimal genus problem for dihedral groups acting on the surfaces described above, for odd genera.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"479-492"},"PeriodicalIF":0.5,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48623154","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 : 2020-09-03DOI: 10.7146/math.scand.a-120288
J. Bassi
Dynamical conditions that guarantee stability for discrete transformation group C∗-algebras are determined. The results are applied to the case of some discrete subgroups of SL(2,R) acting on the punctured plane by means of matrix multiplication of vectors. In the case of cocompact subgroups, further properties of such crossed products are deduced from properties of the C∗-algebra associated to the horocycle flow on the corresponding compact homogeneous space of SL(2,R).
{"title":"On $C^*$-algebras associated to actions of discrete subgroups of $operatorname{SL}(2,mathbb{R})$ on the punctured plane","authors":"J. Bassi","doi":"10.7146/math.scand.a-120288","DOIUrl":"https://doi.org/10.7146/math.scand.a-120288","url":null,"abstract":"Dynamical conditions that guarantee stability for discrete transformation group C∗-algebras are determined. The results are applied to the case of some discrete subgroups of SL(2,R) acting on the punctured plane by means of matrix multiplication of vectors. In the case of cocompact subgroups, further properties of such crossed products are deduced from properties of the C∗-algebra associated to the horocycle flow on the corresponding compact homogeneous space of SL(2,R).","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"540-558"},"PeriodicalIF":0.5,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49027202","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 : 2020-09-03DOI: 10.7146/math.scand.a-121452
David Stapleton
The point of this paper is to give a short, direct proof that rank $2$ toric vector bundles on $n$-dimensional projective space split once $n$ is at least $3$. This result is originally due to Bertin and Elencwajg, and there is also related work by Kaneyama, Klyachko, and Ilten-Süss. The idea is that, after possibly twisting the vector bundle, there is a section which is a complete intersection.
{"title":"A direct proof that toric rank $2$ bundles on projective space split","authors":"David Stapleton","doi":"10.7146/math.scand.a-121452","DOIUrl":"https://doi.org/10.7146/math.scand.a-121452","url":null,"abstract":"The point of this paper is to give a short, direct proof that rank $2$ toric vector bundles on $n$-dimensional projective space split once $n$ is at least $3$. This result is originally due to Bertin and Elencwajg, and there is also related work by Kaneyama, Klyachko, and Ilten-Süss. The idea is that, after possibly twisting the vector bundle, there is a section which is a complete intersection.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45522287","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 : 2020-06-26DOI: 10.7146/math.scand.a-132257
Ville Tengvall
We introduce a certain integrability condition for the reciprocal of the Jacobian determinant which guarantees the local homeomorphism property of quasiregular mappings with a small inner dilatation. This condition turns out to be sharp in the planar case. We also show that every branch point of a quasiregular mapping with a small inner dilatation is a Lebesgue point of the differential matrix of the mapping.
{"title":"Remarks on Martio's conjecture","authors":"Ville Tengvall","doi":"10.7146/math.scand.a-132257","DOIUrl":"https://doi.org/10.7146/math.scand.a-132257","url":null,"abstract":"We introduce a certain integrability condition for the reciprocal of the Jacobian determinant which guarantees the local homeomorphism property of quasiregular mappings with a small inner dilatation. This condition turns out to be sharp in the planar case. We also show that every branch point of a quasiregular mapping with a small inner dilatation is a Lebesgue point of the differential matrix of the mapping.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46163613","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 : 2020-06-25DOI: 10.7146/math.scand.a-128965
J. Christensen, K. Thomsen
We provide a general description of the KMS states for flows whose fixed point algebra satisfies a certain regularity condition. This is then applied to crossed products by discrete groups, and in particular to certain flows on crossed products by discrete abelian groups where the methods can be combined with spectral analysis for abelian automorphism groups.
{"title":"KMS states on crossed products by abelian groups","authors":"J. Christensen, K. Thomsen","doi":"10.7146/math.scand.a-128965","DOIUrl":"https://doi.org/10.7146/math.scand.a-128965","url":null,"abstract":"We provide a general description of the KMS states for flows whose fixed point algebra satisfies a certain regularity condition. This is then applied to crossed products by discrete groups, and in particular to certain flows on crossed products by discrete abelian groups where the methods can be combined with spectral analysis for abelian automorphism groups.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44446577","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 : 2020-05-29DOI: 10.7146/math.scand.a-128520
Ken Kamano, Tomokazu Onozuka
Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute convergence, give some new expressions, and show new relations of the function. We also give a direct proof of the interpolation of Ohno's relation.
{"title":"Analytic properties of Ohno function","authors":"Ken Kamano, Tomokazu Onozuka","doi":"10.7146/math.scand.a-128520","DOIUrl":"https://doi.org/10.7146/math.scand.a-128520","url":null,"abstract":"Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute convergence, give some new expressions, and show new relations of the function. We also give a direct proof of the interpolation of Ohno's relation.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41327308","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 : 2020-05-06DOI: 10.7146/math.scand.a-119699
Sayan Chakraborty
Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibres are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of K0 for all noncommutative tori.
{"title":"Some remarks on $mathrm{K}_0$ of noncommutative tori","authors":"Sayan Chakraborty","doi":"10.7146/math.scand.a-119699","DOIUrl":"https://doi.org/10.7146/math.scand.a-119699","url":null,"abstract":"Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibres are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of K0 for all noncommutative tori.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"387-400"},"PeriodicalIF":0.5,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43947012","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 : 2020-05-06DOI: 10.7146/math.scand.a-119601
H. Mustafayev
Let G be a locally compact abelian group and let M(G) be the measure algebra of G. A measure μ∈M(G) is said to be power bounded if supn≥0∥μn∥1<∞. Let T={Tg:g∈G} be a bounded and continuous representation of G on a Banach space X. For any μ∈M(G), there is a bounded linear operator on X associated with µ, denoted by Tμ, which integrates Tg with respect to µ. In this paper, we study norm and almost everywhere behavior of the sequences {Tnμx} (x∈X) in the case when µ is power bounded. Some related problems are also discussed.
{"title":"On the convergence of iterates of convolution operators in Banach spaces","authors":"H. Mustafayev","doi":"10.7146/math.scand.a-119601","DOIUrl":"https://doi.org/10.7146/math.scand.a-119601","url":null,"abstract":"Let G be a locally compact abelian group and let M(G) be the measure algebra of G. A measure μ∈M(G) is said to be power bounded if supn≥0∥μn∥1<∞. Let T={Tg:g∈G} be a bounded and continuous representation of G on a Banach space X. For any μ∈M(G), there is a bounded linear operator on X associated with µ, denoted by Tμ, which integrates Tg with respect to µ. In this paper, we study norm and almost everywhere behavior of the sequences {Tnμx} (x∈X) in the case when µ is power bounded. Some related problems are also discussed.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"339-366"},"PeriodicalIF":0.5,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48320337","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 : 2020-05-06DOI: 10.7146/math.scand.a-116244
Huiju Wang, P. Niu
In this paper we consider the convex integral functional I:=∫ΩΦ(gu)dμ in the metric measure space (X,d,μ), where X is a set, d is a metric, µ is a Borel regular measure satisfying the doubling condition, Ω is a bounded open subset of X, u belongs to the Orlicz-Sobolev space N1,Φ(Ω), Φ is an N-function satisfying the Δ2-condition, gu is the minimal Φ-weak upper gradient of u. By improving the corresponding method in the Euclidean space to the metric setting, we establish the local boundedness for minimizers of the convex integral functional under the assumption that (X,d,μ) satisfies the (1,1)-Poincare inequality. The result of this paper can be applied to the Carnot-Caratheodory space spanned by vector fields satisfying Hormander's condition.
{"title":"Local boundedness for minimizers of convex integral functionals in metric measure spaces","authors":"Huiju Wang, P. Niu","doi":"10.7146/math.scand.a-116244","DOIUrl":"https://doi.org/10.7146/math.scand.a-116244","url":null,"abstract":"In this paper we consider the convex integral functional I:=∫ΩΦ(gu)dμ in the metric measure space (X,d,μ), where X is a set, d is a metric, µ is a Borel regular measure satisfying the doubling condition, Ω is a bounded open subset of X, u belongs to the Orlicz-Sobolev space N1,Φ(Ω), Φ is an N-function satisfying the Δ2-condition, gu is the minimal Φ-weak upper gradient of u. By improving the corresponding method in the Euclidean space to the metric setting, we establish the local boundedness for minimizers of the convex integral functional under the assumption that (X,d,μ) satisfies the (1,1)-Poincare inequality. The result of this paper can be applied to the Carnot-Caratheodory space spanned by vector fields satisfying Hormander's condition.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"126 1","pages":"259-275"},"PeriodicalIF":0.5,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49286066","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 : 2020-04-18DOI: 10.7146/math.scand.a-126042
J. À. Montaner, F. Planas-Vilanova
Divisors whose Jacobian ideal is of linear type have received a lot of attention recently because of its connections with the theory of $D$-modules. In this work we are interested on divisors of expected Jacobian type, that is, divisors whose gradient ideal is of linear type and the relation type of its Jacobian ideal coincides with the reduction number with respect to the gradient ideal plus one. We provide conditions in order to be able to describe precisely the equations of the Rees algebra of the Jacobian ideal. We also relate the relation type of the Jacobian ideal to some $D$-module theoretic invariant given by the degree of the Kashiwara operator.
{"title":"Divisors of expected Jacobian type","authors":"J. À. Montaner, F. Planas-Vilanova","doi":"10.7146/math.scand.a-126042","DOIUrl":"https://doi.org/10.7146/math.scand.a-126042","url":null,"abstract":"Divisors whose Jacobian ideal is of linear type have received a lot of attention recently because of its connections with the theory of $D$-modules. In this work we are interested on divisors of expected Jacobian type, that is, divisors whose gradient ideal is of linear type and the relation type of its Jacobian ideal coincides with the reduction number with respect to the gradient ideal plus one. We provide conditions in order to be able to describe precisely the equations of the Rees algebra of the Jacobian ideal. We also relate the relation type of the Jacobian ideal to some $D$-module theoretic invariant given by the degree of the Kashiwara operator.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46213898","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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