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Arkiv for Matematik, 2016
ISSN:
0004-2080 (Print)
1871-2487 (Online)
In this year (18 articles)
New Volume, New Issue
[1] Non-conjugacy of maximal abelian diagonalizable subalgebras in extended affine Lie algebras
Uladzimir Yahorau Department of Mathematics, University of Ottawa
Rings and Algebras mathscidoc:1701.01009
Arkiv for Matematik, 1-11, 2015.2
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[2] The Hartogs extension theorem for holomorphic vector bundles and sprays
Rafael B. Andrist Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal Nikolay Shcherbina Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal Erlend F. Wold Matematisk Institutt, Universitet i Oslo
Functional Analysis Geometric Analysis and Geometric Topology mathscidoc:1701.01010
Arkiv for Matematik, 1-21, 2014.12
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We give a detailed proof of Siu’s theorem on extendibility of holomorphic vector bundles of rank larger than one, and prove a corresponding extension theorem for holomorphic sprays. We apply this result to study ellipticity properties of complements of compact subsets in Stein manifolds. In particular we show that the complement of a closed ball in $\mathbb{C}^{n}, n \geq3$ , is not subelliptic.
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[3] On improved fractional Sobolev–Poincaré inequalities
Bartłomiej Dyda Faculty of Pure and Applied Mathematics, Wrocław University of Technology Lizaveta Ihnatsyeva Department of Mathematics, Kansas State University Antti V. Vähäkangas Department of Mathematics and Statistics, University of Jyvaskyla
Analysis of PDEs Functional Analysis mathscidoc:1701.03014
Arkiv for Matematik, 1-18, 2014.5
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We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a ‘separation property’, is a John domain.
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[4] On the Szegö kernel of Cartan–Hartogs domains
Andrea Loi Dipartimento di Matematica e Informatica, Università di Cagliari Daria Uccheddu Dipartimento di Matematica e Informatica, Università di Cagliari Michela Zedda Dipartimento di Matematica “G. Peano”, Università di Torino
Differential Geometry mathscidoc:1701.10007
Arkiv for Matematik, 1-12, 2014.10
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Inspired by the work of Z. Lu and G. Tian (Duke Math. J. 125:351–387,2004) in the compact setting, in this paper we address the problem of studying the Szegö kernel of the disk bundle over a noncompact Kähler manifold. In particular we compute the Szegö kernel of the disk bundle over a Cartan–Hartogs domain based on a bounded symmetric domain. The main ingredients in our analysis are the fact that every Cartan–Hartogs domain can be viewed as an “iterated” disk bundle over its base and the ideas given in (Arezzo, Loi and Zuddas in Math. Z. 275:1207–1216,2013) for the computation of the Szegö kernel of the disk bundle over an Hermitian symmetric space of compact type.
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[5] Reducibility of invertible tuples to the principal component in commutative Banach algebras
Raymond Mortini Département de Mathématiques et Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine Rudolf Rupp Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, TH-Nürnberg
Functional Analysis Spectral Theory and Operator Algebra mathscidoc:1701.12009
Arkiv for Matematik, 1-26, 2014.12
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Let $A$ be a complex, commutative unital Banach algebra. We introduce two notions of exponential reducibility of Banach algebra tuples and present an analogue to the Corach-Suárez result on the connection between reducibility in $A$ and in $C(M(A))$ . Our methods are of an analytical nature. Necessary and sufficient geometric/topological conditions are given for reducibility (respectively reducibility to the principal component of $U_{n}(A)$ ) whenever the spectrum of $A$ is homeomorphic to a subset of $\mathbb{C}^{n}$ .
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[6] The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures
Alexander I. Bufetov Aix-Marseille Université, Centrale Marseille, CNRS, I2M, UMR7373, 39 Rue F. Joliot Curie, Marseille Cedex 13, France Yanqi Qiu Aix-Marseille Université, Centrale Marseille, CNRS, I2M, UMR7373, 39 Rue F. Joliot Curie, Marseille Cedex 13, France
Analysis of PDEs Functional Analysis mathscidoc:1701.03015
Arkiv for Matematik, 1-33, 2015.1
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The main result of this paper, Theorem 1.5, gives explicit formulae for the kernels of the ergodic decomposition measures for infinite Pickrell measures on the space of infinite complex matrices. The kernels are obtained as the scaling limits of Christoffel-Uvarov deformations of Jacobi orthogonal polynomial ensembles.
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[7] The Loewner equation for multiple slits, multiply connected domains and branch points
Christoph Böhm Institut für Mathematik, Universität Würzburg Sebastian Schleißinger Dipartimento di Matematica, Università di Roma “Tor Vergata”
Classical Analysis and ODEs mathscidoc:1701.05002
Arkiv for Matematik, 1-32, 2014.10
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[8] Stable hypersurfaces with zero scalar curvature in Euclidean space
Hilário Alencar Instituto de Matemática, Universidade Federal de Alagoas Manfredo do Carmo Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, RJ, Brazil Gregório Silva Neto Instituto de Matemática, Universidade Federal de Alagoas
Analysis of PDEs Differential Geometry mathscidoc:1701.03016
Arkiv for Matematik, 1-9, 2015.9
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In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete stable hypersurface with zero scalar curvature, polynomial growth of integral of the mean curvature, and with the Gauss-Kronecker curvature bounded away from zero. We conclude this paper giving a sufficient condition for a regular domain to be stable in terms of the mean and the Gauss-Kronecker curvatures of the hypersurface and the radius of the smallest extrinsic ball which contains the domain.
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[9] A geometric interpretation of the Schützenberger group of a minimal subshift
Jorge Almeida CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto Alfredo Costa CMUC, Department of Mathematics, University of Coimbra
Geometric Analysis and Geometric Topology Group Theory and Lie Theory mathscidoc:1701.01011
Arkiv for Matematik, 1-33, 2015.7
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The first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geometric considerations involving the Rauzy graphs of the subshift. Indeed, the group is shown to be isomorphic to the inverse limit of the profinite completions of the fundamental groups of the Rauzy graphs of the subshift. A further result involving geometric arguments on Rauzy graphs is a criterion for freeness of the profinite group of a minimal subshift based on the Return Theorem of Berthé et al.
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[10] Stiefel-Whitney classes of curve covers
Björn Selander Tomtebogatan 18, Stockholm, Sweden
K-Theory and Homology mathscidoc:1701.01012
Arkiv for Matematik, 1-18, 2013.10
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Let $D$ be a Dedekind scheme with the characteristic of all residue fields not equal to 2. To every tame cover $C\to D$ with only odd ramification we associate a second Stiefel-Whitney class in the second cohomology with mod 2 coefficients of a certain tame orbicurve $[D]$ associated to $D$ . This class is then related to the pull-back of the second Stiefel-Whitney class of the push-forward of the line bundle of half of the ramification divisor. This shows (indirectly) that our Stiefel-Whitney class is the pull-back of a sum of cohomology classes considered by Esnault, Kahn and Viehweg in ‘Coverings with odd ramification and Stiefel-Whitney classes’. Perhaps more importantly, in the case of a proper and smooth curve over an algebraically closed field, our Stiefel-Whitney class is shown to be the pull-back of an invariant considered by Serre in ‘Revêtements à ramification impaire et thêta-caractéristiques’, and in this case our arguments give a new proof of the main result of that article.
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[11] Families of Gorenstein and almost Gorenstein rings
V. Barucci Dipartimento di Matematica, Sapienza - Università di Roma M. D’Anna Dipartimento di Matematica e Informatica, Università degli Studi di Catania F. Strazzanti Dipartimento di Matematica, Università di Pisa
Rings and Algebras mathscidoc:1701.31002
Arkiv for Matematik, 1-18, 2015.12
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Starting with a commutative ring $R$ and an ideal $I$ , it is possible to define a family of rings $R(I)_{a,b}$ , with $a,b \in R$ , as quotients of the Rees algebra $\oplus_{n \geq0} I^{n}t^{n}$ ; among the rings appearing in this family we find Nagata’s idealization and amalgamated duplication. Many properties of these rings depend only on $R$ and $I$ and not on $a$ , $b$ ; in this paper we show that the Gorenstein and the almost Gorenstein properties are independent of $a$ , $b$ . More precisely, we characterize when the rings in the family are Gorenstein, complete intersection, or almost Gorenstein and we find a formula for the type.
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[12] Euler sequence and Koszul complex of a module
Björn Andreas Mathematisches Institut, Freie Universität Berlin Darío Sánchez Gómez Departamento de Matemáticas and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca Fernando Sancho de Salas Departamento de Matemáticas and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca
K-Theory and Homology mathscidoc:1701.01013
Arkiv for Matematik, 1-21, 2016.1
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We construct relative and global Euler sequences of a module. We apply it to prove some acyclicity results of the Koszul complex of a module and to compute the cohomology of the sheaves of (relative and absolute) differential $p$ -forms of a projective bundle. In particular we generalize Bott’s formula for the projective space to a projective bundle over a scheme of characteristic zero.
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[13] Fourier dimension of random images
Fredrik Ekström Centre for Mathematical Sciences, Lund University
Functional Analysis mathscidoc:1701.12010
Arkiv for Matematik, 1-17, 2016.2
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Given a compact set of real numbers, a random $C^{m + \alpha}$ -diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number $s$ , almost surely has Fourier dimension greater than or equal to $s / (m + \alpha)$ . This is used to show that every Borel subset of the real numbers of Hausdorff dimension $s$ is $C^{m + \alpha}$ -equivalent to a set of Fourier dimension greater than or equal to $s / (m + \alpha )$ . In particular every Borel set is diffeomorphic to a Salem set, and the Fourier dimension is not invariant under $C^{m}$ -diffeomorphisms for any $m$ .
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[14] Restrictions of Riesz–Morrey potentials
David R. Adams Department of Mathematics, University of Kentucky Jie Xiao Department of Mathematics and Statistics, Memorial University
Functional Analysis mathscidoc:1701.12011
Arkiv for Matematik, 1-31, 2015.11
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[15] The dual of Brown representability for some derived categories
George Ciprian Modoi Faculty of Mathematics and Computer Science, Babeş-Bolyai University
Category Theory mathscidoc:1701.04002
Arkiv for Matematik, 1-14, 2016.2
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Consider a complete abelian category which has an injective cogenerator. If its derived category is left-complete we show that the dual of this derived category satisfies Brown representability. In particular, this is true for the derived category of an abelian AB $4^{*}$ - $n$ category and for the derived category of quasi-coherent sheaves over a nice enough scheme, including the projective finitely dimensional space.
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[16] Non-separability of the Gelfand space of measure algebras
Przemysław Ohrysko Institute of Mathematics, Polish Academy of Sciences Michał Wojciechowski Institute of Mathematics, Polish Academy of Sciences Colin C. Graham Department of Mathematics, University of British Columbia
Representation Theory Rings and Algebras mathscidoc:1701.30003
Arkiv for Matematik, 1-11, 2016.2
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We prove that there exists uncountably many pairwise disjoint open subsets of the Gelfand space of the measure algebra on any locally compact non-discrete abelian group which shows that this space is not separable (in fact, we prove this assertion for the ideal $M_{0}(G)$ consisting of measures with Fourier-Stieltjes transforms vanishing at infinity which is a stronger statement). As a corollary, we obtain that the spectras of elements in the algebra of measures cannot be recovered from the image of one countable subset of the Gelfand space under Gelfand transform, common for all elements in the algebra.
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[17] Directional Poincaré inequalities along mixing flows
Stefan Steinerberger Department of Mathematics, Yale University
Analysis of PDEs Differential Geometry mathscidoc:1701.03017
Arkiv for Matematik, 1-15, 2015.11
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We provide a refinement of the Poincaré inequality on the torus $\mathbb{T}^{d}$ : there exists a set $\mathcal{B} \subset \mathbb{T} ^{d}$ of directions such that for every $\alpha \in \mathcal{B}$ there is a $c_{\alpha } > 0$ with $$\begin{aligned} \|\nabla f\|_{L^{2}(\mathbb{T}^{d})}^{d-1} \| \langle \nabla f, \alpha \rangle \|_{L^{2}(\mathbb{T}^{d})} \geq c_{\alpha }\|f\| _{L^{2}(\mathbb{T}^{d})}^{d} \quad \mbox{for all}~f\in H^{1}\bigl( \mathbb{T}^{d}\bigr)~ \mbox{with mean 0.} \end{aligned}$$ The derivative $\langle \nabla f, \alpha \rangle $ does not detect any oscillation in directions orthogonal to $\alpha $ , however, for certain $\alpha $ the geodesic flow in direction $\alpha $ is sufficiently mixing to compensate for that defect. On the two-dimensional torus $\mathbb{T}^{2}$ the inequality holds for $\alpha = (1, \sqrt{2})$ but is not true for $\alpha = (1,e)$ . Similar results should hold at a great level of generality on very general domains.
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[18] Modules of systems of measures on polarizable Carnot groups
M. Brakalova Department of Mathematics, Fordham University I. Markina Department of Mathematics, University of Bergen A. Vasil’ev Department of Mathematics, University of Bergen
Group Theory and Lie Theory mathscidoc:1701.17002
Arkiv for Matematik, 1-31, 2015.8
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Impact Factor
0.744
Available
1949 - 2016
Volumes
60
Issues
119
Articles
1382