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Arkiv for Matematik, 2014, Volume 53
ISSN:
0004-2080 (Print)
1871-2487 (Online)
In this volume (18 articles)
Issue 1
[1] Approximation numbers of composition operators on the Dirichlet space
Pascal Lefèvre Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956 Faculté des Sciences Jean Perrin, Université Lille-Nord-de-France UArtois Daniel Li Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956 Faculté des Sciences Jean Perrin, Université Lille-Nord-de-France UArtois Hervé Queffélec Laboratoire Paul Painlevé U.M.R. CNRS 8524, Université Lille-Nord-de-France USTL Luis Rodríguez-Piazza Facultad de Matemáticas, Departamento de Análisis Matemático & IMUS, Universidad de Sevilla
Functional Analysis mathscidoc:1701.12026
Arkiv for Matematik, 53, (1), 155-175, 2013.2
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Benazouz H, Elfallah O, Kellay K, et al. Contact points and Schatten composition operators[J]. Mathematische Zeitschrift, 2014: 407-422.
2
Elfallah O, Mahzouli H, Marrhich I, et al. Asymptotic behavior of eigenvalues of Toeplitz operators on the weighted analytic spaces[J]. Journal of Functional Analysis, 2016, 270(12): 4614-4630.
3
Li D, Queffelec H, Rodriguezpiazza L, et al. A spectral radius type formula for approximation numbers of composition operators[J]. Journal of Functional Analysis, 2014, 267(12): 4753-4774.
4
Li D, Queffelec H, Rodriguezpiazza L, et al. Two remarks on composition operators on the Dirichlet space[J]. Journal of Mathematical Analysis and Applications, 2014, 426(2): 734-746.
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Benazouz H, Elfallah O, Kellay K, et al. Contact points and Schatten composition operators[J]. Mathematische Zeitschrift, 2014: 407-422.
6
Zohra Bendaoud · F Korrichi · L Merghni · Abu Elgasim A Yagoub · Centrale Marseille · Mostafa Mbekhta. Estimates of Generalized Nevanlinna Counting Function and Applications to Composition Operators. 2015.
Abstract
We study the decay of approximation numbers of compact composition operators on the Dirichlet space. We give upper and lower bounds for these numbers. In particular, we improve on a result of El-Fallah, Kellay, Shabankhah and Youssfi, on the set of contact points with the unit circle of a compact symbolic composition operator acting on the Dirichlet space $\mathcal{D}$ . We extend their results in two directions: first, the contact only takes place at the point 1. Moreover, the approximation numbers of the operator can be arbitrarily subexponentially small.
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[2] On the order map for hypersurface coamoebas
Jens Forsgård Department of Mathematics, Stockholm University Petter Johansson Department of Mathematics, Stockholm University
Complex Variables and Complex Analysis mathscidoc:1701.08012
Arkiv for Matematik, 53, (1), 79-104, 2013.2
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Kiselman C O. Questions inspired by Mikael Passare’s mathematics[C]., 2012, 25(2): 271-288.
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Forsgard J, Johansson P. Coamoebas and line arrangements in dimension two[J]. Mathematische Zeitschrift, 2014: 25-38.
3
Thorsten Jorgens · Thorsten Theobald · Timo De Wolff. Imaginary projections of polynomials. 2016.
4
Petter Johansson · Hakan Samuelsson Kalm. A Ronkin type function for coamoebas. 2014.
Abstract
Given a hypersurface coamoeba of a Laurent polynomial$f$, it is an open problem to describe the structure of the set of connected components of its complement. In this paper we approach this problem by introducing the lopsided coamoeba. We show that the closed lopsided coamoeba comes naturally equipped with an order map, i.e. a map from the set of connected components of its complement to a translated lattice inside the zonotope of a Gale dual of the point configuration $\operatorname{supp}(f)$ . Under a natural assumption, this map is a bijection. Finally we use this map to obtain new results concerning coamoebas of polynomials of small codimension.
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[3] The Alexander polynomial as quantum invariant of links
Antonio Sartori Mathematisches Institut, Universität Bonn
Quantum Algebra Representation Theory mathscidoc:1701.29004
Arkiv for Matematik, 53, (1), 177-202, 2013.8
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Hoel Queffelec · Antonio Sartori. Mixed quantum skew Howe duality and link invariants of type A. 2015.
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Antonio Sartoriaffiliated Withmathematisches Institut. Categorification of tensor powers of the vector representation of \(U_q({\mathfrak {gl}}(1|1))\). 2016.
3
Beliakova A, Guliyev Z, Habiro K, et al. Trace as an alternative decategorification functor[C]., 2014, 39(4): 425-480.
Abstract
In these notes we collect some results about finite-dimensional representations of $U_{q}(\mathfrak {gl}(1\mid1))$ and related invariants of framed tangles, which are well-known to experts but difficult to find in the literature. In particular, we give an explicit description of the ribbon structure on the category of finite-dimensional $U_{q}(\mathfrak {gl}(1\mid1))$ -representations and we use it to construct the corresponding quantum invariant of framed tangles. We explain in detail why this invariant vanishes on closed links and how one can modify the construction to get a non-zero invariant of framed closed links. Finally we show how to obtain the Alexander polynomial by considering the vector representation of $U_{q}(\mathfrak {gl}(1\mid1))$ .
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[4] Hausdorff dimension of wiggly metric spaces
Jonas Azzam Department of Mathematics, University of Washington-Seattle
Functional Analysis Metric Geometry mathscidoc:1701.12027
Arkiv for Matematik, 53, (1), 1-36, 2013.3
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For a compact connected set$X$⊆$ℓ$^{∞}, we define a quantity$β$′($x$,$r$) that measures how close$X$may be approximated in a ball$B$($x$,$r$) by a geodesic curve. We then show that there is$c$>0 so that if$β$′($x$,$r$)>$β$>0 for all$x$∈$X$and$r$<$r$_{0}, then $\operatorname{dim}X>1+c\beta^{2}$ . This generalizes a theorem of Bishop and Jones and answers a question posed by Bishop and Tyson.
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[5] On normal forms for Levi-flat hypersurfaces with an isolated line singularity
Arturo Fernández-Pérez Departamento de Matemática, Universidade Federal de Minas Gerais
mathscidoc:1701.01022
Arkiv for Matematik, 53, (1), 65-78, 2013.4
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We prove the existence of normal forms for some local real-analytic Levi-flat hypersurfaces with an isolated line singularity. We also give sufficient conditions for a Levi-flat hypersurface with a complex line as singularity to be a pullback of a real-analytic curve in $\mathbb{C}$ via a holomorphic function.
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[6] Regularity of the local fractional maximal function
Toni Heikkinen Department of Mathematics, P.O. Box 11100, Aalto University, Finland Juha Kinnunen Department of Mathematics, P.O. Box 11100, Aalto University, Finland Janne Korvenpää Department of Mathematics, P.O. Box 11100, Aalto University, Finland Heli Tuominen Department of Mathematics and Statistics, P.O. Box 35, University of Jyväskylä, Finland
Functional Analysis mathscidoc:1701.12028
Arkiv for Matematik, 53, (1), 127-154, 2013.10
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This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply norm estimates in Sobolev spaces. An unexpected feature is that these estimates contain extra terms involving spherical and fractional maximal functions. Moreover, we construct several explicit examples, which show that our results are essentially optimal. Extensions to metric measure spaces are also discussed.
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[7] Exact Lagrangian caps and non-uniruled Lagrangian submanifolds
Georgios Dimitroglou Rizell Département de Mathématiques, Université Paris-Sud
Geometric Analysis and Geometric Topology Symplectic Geometry mathscidoc:1701.15006
Arkiv for Matematik, 53, (1), 37-64, 2013.6
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We make the elementary observation that the Lagrangian submanifolds of$C$^{$n$},$n$≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov–Eliashberg algebra is acyclic.
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[8] Uniform exponential stability of the Ekman spiral
Yoshikazu Giga Graduate School of Mathematical Sciences, University of Tokyo Jürgen Saal Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf
Analysis of PDEs mathscidoc:1701.03031
Arkiv for Matematik, 53, (1), 105-126, 2013.5
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This paper studies stability of the Ekman boundary layer. We utilize a new approach, developed by the authors in a precedent paper, based on Fourier transformed finite vector Radon measures, which yields exponential stability of the Ekman spiral. By this method we can also derive very explicit bounds for solutions of the linearized and the nonlinear Ekman systems. For example, we can prove these bounds to be uniform with respect to the angular velocity of rotation, which has proved to be relevant for several aspects. Another advantage of this approach is that we obtain well-posedness in classes containing nondecaying vector fields such as almost periodic functions. These outcomes give respect to the nature of boundary layer problems and cannot be obtained by approaches in standard function spaces such as Lebesgue, Bessel-potential, Hölder or Besov spaces.
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Issue 2
[1] A note on the singularity category of an endomorphism ring
Xiao-Wu Chen School of Mathematical Sciences, University of Science and Technology of China
Category Theory Rings and Algebras mathscidoc:1701.04004
Arkiv for Matematik, 53, (2), 237-248, 2013.12
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We propose the notion of partial resolution of a ring, which is by definition the endomorphism ring of a certain generator of the given ring. We prove that the singularity category of the partial resolution is a quotient of the singularity category of the given ring. Consequences and examples are given.
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[2] Riemann’s zeta-function and the divisor problem. III
Matti Jutila Department of Mathematics and Statistics, University of Turku
Number Theory mathscidoc:1701.24008
Arkiv for Matematik, 53, (2), 303-315, 2014.3
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Ivic A. On the divisor function and the Riemann zeta-function in short intervals[J]. Ramanujan Journal, 2007, 19(2): 207-224.
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Tsang K. Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function[J]. Science China-mathematics, 2010, 53(9): 2561-2572.
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Huxley M N, Ivic A. Subconvexity for the Riemann zeta-function and the divisor problem[C]., 2006.
4
Ivic A. Some remarks on the moments of \\left| {\\varsigma \\left( {\\tfrac{1}{2} + it} \\right)} \\right| in short intervals[J]. Acta Mathematica Hungarica, 2007: 15-24.
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Yann Bugeaud · Aleksandar Ivic. Sums of the error term function in the mean square for ζ(s). 2008.
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Aleksandar Ivic. Some remarks on the moments of % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfM…. 2008.
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Ivic A. On the mean square of the Riemann zeta-function in short intervals[J]. Publications De L\u0027institut Mathematique, 2008, 85(99): 1-17.
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Aleksandar Ivic. The Mean Values of the Riemann Zeta-Function on the Critical Line. 2014.
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Aleksandar Ivic. Some remarks on the moments of <img src="/fulltext-image.asp?format=htmlnonpaginated&src=F473557533. 2008.
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Aleksandar Ivic. Hybrid Moments of the Riemann Zeta-Function. 2008.
Abstract
In two earlier papers with the same title, we studied connections between Voronoi’s formula in the divisor problem and Atkinson’s formula for the mean square of Riemann’s zeta-function. Now we consider this correspondence in terms of segments of sums appearing in these formulae and show that a certain arithmetic conjecture concerning the divisor function implies best possible bounds for the classical error terms Δ($x$) and$E$($T$).
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[3] Un scindage du morphisme de Frobenius quantique
Michel Gros IRMAR, Université de Rennes I Masaharu Kaneda Department of Mathematics, Osaka City University
Quantum Algebra mathscidoc:1701.29005
Arkiv for Matematik, 53, (2), 271-301, 2014.8
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Nous montrons que le morphisme de Frobenius quantique construit par Lusztig dans le cadre des algèbres enveloppantes quantiques $U_{\mathcal{B}}$ spécialisées en une racine de l’unité admet un scindage multiplicatif (non unitaire). Nous utilisons pour ce faire une base de la partie torique de la petite algèbre quantique constituée d’idempotents orthogonaux deux à deux et de somme 1 et faisons de même dans le cas «modulaire» pour l’algèbre des distributions d’un groupe algébrique semi-simple.
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[4] A classification result for helix surfaces with parallel mean curvature in product spaces
Dorel Fetcu Department of Mathematics and Informatics, Gh. Asachi Technical University of Iaşi
Differential Geometry mathscidoc:1701.10016
Arkiv for Matematik, 53, (2), 249-258, 2014.1
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[5] Extremal functions for real convex bodies
Daniel M. Burns Department of Mathematics, University of Michigan Norman Levenberg Department of Mathematics, Indiana University Sione Ma‘u Department of Mathematics, University of Auckland
Convex and Discrete Geometry mathscidoc:1701.40001
Arkiv for Matematik, 53, (2), 203-236, 2013.12
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We study the smoothness of the Siciak–Zaharjuta extremal function associated to a convex body in $\mathbb{R}^{2}$ . We also prove a formula relating the complex equilibrium measure of a convex body in $\mathbb{R}^{n}$ ($n$≥2) to that of its Robin indicatrix. The main tool we use is extremal ellipses.
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[6] On Möbius orthogonality for interval maps of zero entropy and orientation-preserving circle homeomorphisms
Davit Karagulyan Department of Mathematics, KTH Royal Institute of Technology
Dynamical Systems mathscidoc:1701.11012
Arkiv for Matematik, 53, (2), 317-327, 2013.12
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[7] Fatou–Bieberbach domains in $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$
Franc Forstnerič Faculty of Mathematics and Physics, University of Ljubljana Erlend F. Wold Department of Mathematics, University of Oslo
Functional Analysis mathscidoc:1701.12029
Arkiv for Matematik, 53, (2), 259-270, 2014.1
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We construct Fatou–Bieberbach domains in $\mathbb{C}^{n}$ for$n$>1 which contain a given compact set$K$and at the same time avoid a totally real affine subspace$L$of dimension <$n$, provided that$K$∪$L$is polynomially convex. By using this result, we show that the domain $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$ for 1≤$k$<$n$enjoys the basic Oka property with approximation for maps from any Stein manifold of dimension <$n$.
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[8] Mappings onto multiplicative subsets of function algebras and spectral properties of their products
Takeshi Miura Department of Mathematics Faculty of Science, Niigata University Thomas Tonev Department of Mathematical Sciences, University of Montana
Spectral Theory and Operator Algebra mathscidoc:1701.32006
Arkiv for Matematik, 53, (2), 329-358, 2014.4
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We characterize mappings$S$_{$i$}and$T$_{$i$}, not necessarily linear, from sets $\mathcal {J}_{i}$ ,$i$=1,2, onto multiplicative subsets of function algebras, subject to the following conditions on the peripheral spectra of their products:$σ$_{$π$}($S$_{1}($a$)$S$_{2}($b$))⊂$σ$_{$π$}($T$_{1}($a$)$T$_{2}($b$)) and$σ$_{$π$}($S$_{1}($a$)$S$_{2}($b$))∩$σ$_{$π$}($T$_{1}($a$)$T$_{2}($b$))≠∅, $a\in \mathcal {J}_{1}$ , $b\in \mathcal {J}_{2}$ . As a direct consequence we obtain a large number of previous results about mappings subject to various spectral conditions.
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[9] Unicity of graded covers of the category $\mathcal{O}$ of Bernstein–Gelfand–Gelfand
Michael Rottmaier Mathematical Institute, University of Freiburg Wolfgang Soergel Mathematical Institute, University of Freiburg
Category Theory Representation Theory mathscidoc:1701.04005
Arkiv for Matematik, 53, (2), 383-400, 2014.4
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[10] Singular hermitian metrics on holomorphic vector bundles
Hossein Raufi Department of Mathematics Chalmers Institute of Technology, and University of Gothenburg
Complex Variables and Complex Analysis Differential Geometry mathscidoc:1701.08013
Arkiv for Matematik, 53, (2), 359-382, 2014.1
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We introduce and study the notion of singular hermitian metrics on holomorphic vector bundles, following Berndtsson and Păun. We define what it means for such a metric to be positively and negatively curved in the sense of Griffiths and investigate the assumptions needed in order to locally define the curvature Θ^{$h$}as a matrix of currents. We then proceed to show that such metrics can be regularised in such a way that the corresponding curvature tensors converge weakly to Θ^{$h$}. Finally we define what it means for$h$to be strictly negatively curved in the sense of Nakano and show that it is possible to regularise such metrics with a sequence of smooth, strictly Nakano negative metrics.
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Impact Factor
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Available
1949 - 2016
Volumes
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Issues
119
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1382