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Arkiv for Matematik, 2007, Volume 46
ISSN:
0004-2080 (Print)
1871-2487 (Online)
In this volume (21 articles)
Issue 1
[1] Convexity of the median in the gamma distribution
Christian Berg Department of Mathematics, University of Copenhagen Henrik L. Pedersen Department of Natural Sciences, University of Copenhagen
TBD mathscidoc:1701.333116
Arkiv for Matematik, 46, (1), 1-6, 2006.10
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[2] Componentwise linear ideals with minimal or maximal Betti numbers
Jürgen Herzog Fachbereich Mathematik und Informatik, Universität Duisburg-Essen Takayuki Hibi Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University Satoshi Murai Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University Yukihide Takayama Department of Mathematical Sciences, Ritsumeikan University
TBD mathscidoc:1701.333117
Arkiv for Matematik, 46, (1), 69-75, 2006.11
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[3] Extreme Jensen measures
Sylvain Roy Département de mathématiques, Université Laval
TBD mathscidoc:1701.333118
Arkiv for Matematik, 46, (1), 153-182, 2006.3
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Let Ω be an open subset of$R$^{$d$},$d$≥2, and let$x$∈Ω. A$Jensen measure$for$x$on Ω is a Borel probability measure μ, supported on a compact subset of Ω, such that ∫$u$$d$μ≤$u$($x$) for every superharmonic function$u$on Ω. Denote by$J$_{$x$}(Ω) the family of Jensen measures for$x$on Ω. We present two characterizations of ext($J$_{$x$}(Ω)), the set of extreme elements of$J$_{$x$}(Ω). The first is in terms of finely harmonic measures, and the second as limits of harmonic measures on decreasing sequences of domains.
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[4] Rationally convex sets on the unit sphere in ℂ^{2}
John Wermer Mathematics Department, Brown University
TBD mathscidoc:1701.333119
Arkiv for Matematik, 46, (1), 183-196, 2006.2
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[5] Weighted integral formulas on manifolds
Elin Götmark Department of Mathematics, Chalmers University of Technology and Göteborg University
TBD mathscidoc:1701.333120
Arkiv for Matematik, 46, (1), 43-68, 2006.11
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We present a method of finding weighted Koppelman formulas for ($p$,$q$)-forms on$n$-dimensional complex manifolds$X$which admit a vector bundle of rank$n$over$X$×$X$, such that the diagonal of$X$×$X$has a defining section. We apply the method to ℙ^{$n$}and find weighted Koppelman formulas for ($p$,$q$)-forms with values in a line bundle over ℙ^{$n$}. As an application, we look at the cohomology groups of ($p$,$q$)-forms over ℙ^{$n$}with values in various line bundles, and find explicit solutions to the $\overline{\partial}$ -equation in some of the trivial groups. We also look at cohomology groups of (0,$q$)-forms over ℙ^{$n$}×ℙ^{$m$}with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds.
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[6] The injectivity of the extended Gauss map of general projections of smooth projective varieties
Marc Coppens Departement Industrieel Ingenieur en Biotechniek, Katholieke Hogeschool Kempen
TBD mathscidoc:1701.333121
Arkiv for Matematik, 46, (1), 31-41, 2005.12
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Let$X$be a smooth$n$-dimensional projective variety embedded in some projective space ℙ^{$N$}over the field ℂ of the complex numbers. Associated with the general projection of$X$to a space ℙ^{$N$-$m$}($N$-$m$>$n$+1) one defines an extended Gauss map $\overline{\gamma}\colon\overline{X}\rightarrow\text{Gr}(n;N-m)$ (in case$N$-$m$>2$n$-1 this is the Gauss map of the image of$X$under the projection). We prove that $\overline{X}$ is smooth. In case any two different points of$X$do have disjoint tangent spaces then we prove that $\overline{\gamma}$ is injective.
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[7] Graph Laplacians and topology
Pavel Kurasov Department of Mathematics LTH, Lund University
TBD mathscidoc:1701.333122
Arkiv for Matematik, 46, (1), 95-111, 2006.6
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Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same characteristics are determined by the scattering data consisting of the scattering matrix and the discrete eigenvalues.
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[8] Geometry of spaces of compact operators
Åsvald Lima Department of Mathematics, University of Agder Vegard Lima Department of Mathematics, University of Missouri–Columbia
TBD mathscidoc:1701.333123
Arkiv for Matematik, 46, (1), 113-142, 2006.3
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We introduce the notion of compactly locally reflexive Banach spaces and show that a Banach space$X$is compactly locally reflexive if and only if $\mathcal{K}(Y,X^{**})\subseteq\mathcal{K}(Y,X)^{**}$ for all reflexive Banach spaces$Y$. We show that$X$^{*}has the approximation property if and only if$X$has the approximation property and is compactly locally reflexive. The weak metric approximation property was recently introduced by Lima and Oja. We study two natural weak compact versions of this property. If$X$is compactly locally reflexive then these two properties coincide. We also show how these properties are related to the compact approximation property and the compact approximation property with conjugate operators for dual spaces.
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[9] Decomposable symmetric mappings between infinite-dimensional spaces
Christopher Boyd School of Mathematical Sciences, University College Dublin Silvia Lassalle Departamento de Matemática, Pab. I – Ciudad Universitaria (FCEN), Universidad de Buenos Aires
TBD mathscidoc:1701.333124
Arkiv for Matematik, 46, (1), 7-29, 2006.9
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Decomposable mappings from the space of symmetric$k$-fold tensors over$E$, $\bigotimes_{s,k}E$ , to the space of$k$-fold tensors over$F$, $\bigotimes_{s,k}F$ , are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable mapping belongs to a given operator ideal, then so does its inducing operator. This result allows us to classify injective linear operators between spaces of homogeneous approximable polynomials and between spaces of nuclear polynomials which map rank-1 polynomials to rank-1 polynomials.
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[10] Sharp estimates for maximal operators associated to the wave equation
Keith M. Rogers Departamento de Matemáticas, Universidad Autónoma de Madrid Paco Villarroya University of California, Los Angeles, CA, USA
TBD mathscidoc:1701.333125
Arkiv for Matematik, 46, (1), 143-151, 2006.10
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The wave equation, ∂_{$tt$}$u$=Δ$u$, in ℝ^{$n$+1}, considered with initial data$u$($x$,0)=$f$∈$H$^{$s$}(ℝ^{$n$}) and$u$’($x$,0)=0, has a solution which we denote by $\frac{1}{2}(e^{it\sqrt{-\Delta}}f+e^{-it\sqrt{-\Delta}}f)$ . We give almost sharp conditions under which $\sup_{0<t<1}|e^{\pm it\sqrt{-\Delta}}f|$ and $\sup_{t\in\mathbb{R}}|e^{\pm it\sqrt{-\Delta}}f|$ are bounded from$H$^{$s$}(ℝ^{$n$}) to$L$^{$q$}(ℝ^{$n$}).
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[11] Maximal regularity via reverse Hölder inequalities for elliptic systems of$n$-Laplace type involving measures
Tero Kilpeläinen Department of Mathematics and Statistics, University of Jyväskylä Nageswari Shanmugalingam Department of Mathematical Sciences, University of Cincinnati Xiao Zhong Department of Mathematics and Statistics, University of Jyväskylä
TBD mathscidoc:1701.333126
Arkiv for Matematik, 46, (1), 77-93, 2006.11
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In this note, we consider the regularity of solutions of the nonlinear elliptic systems of$n$-Laplacian type involving measures, and prove that the gradients of the solutions are in the weak Lebesgue space$L$^{$n$,∞}. We also obtain the$a priori$global and local estimates for the$L$^{$n$,∞}-norm of the gradients of the solutions without using BMO-estimates. The proofs are based on a new lemma on the higher integrability of functions.
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Issue 2
[1] Power weighted$L$^{$p$}-inequalities for Laguerre–Riesz transforms
Eleonor Harboure IMAL-FIQ, CONICET, Universidad Nacional del Litoral Carlos Segovia Instituto Argentino de Matemática (IAM), CONICET, Saavedra 15, Ciudad Autónoma de Buenos Aires, Argentina José L. Torrea Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid Beatriz Viviani IMAL-FIQ, CONICET, Universidad Nacional del Litoral
TBD mathscidoc:1701.333127
Arkiv for Matematik, 46, (2), 285-313, 2006.12
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In this paper we give a complete description of the power weighted inequalities, of strong, weak and restricted weak type for the pair of Riesz transforms associated with the Laguerre function system $\{\mathcal{L}_k^{\alpha}\}$ , for any given α>-1. We achieve these results by a careful estimate of the kernels: near the diagonal we show that they are local Calderón–Zygmund operators while in the complement they are majorized by Hardy type operators and the maximal heat-diffusion operator. We also show that in all the cases our results are sharp.
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[2] Gorenstein injective and projective modules and actions of finite-dimensional Hopf algebras
Juan Antonio López-Ramos Departamento de Algebra y Análisis Matemático, Universidad de Almería
TBD mathscidoc:1701.333128
Arkiv for Matematik, 46, (2), 349-361, 2006.12
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[3] Lipschitz continuity of the Green function in Denjoy domains
Tom Carroll Department of Mathematics, National University of Ireland Stephen J. Gardiner School of Mathematical Sciences, University College Dublin
TBD mathscidoc:1701.333129
Arkiv for Matematik, 46, (2), 271-283, 2006.8
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[4] Carleson measures for the generalized Bergman spaces via a T(1)-type theorem
Edgar Tchoundja Département de Mathématiques, Faculté des Sciences de l’Université de Yaoundé I
TBD mathscidoc:1701.333130
Arkiv for Matematik, 46, (2), 377-406, 2007.5
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In this paper, we give a new characterization of Carleson measures for the generalized Bergman spaces. We show first that this problem is equivalent to a T(1)-type problem. Using an idea of Verdera (see [V]), we introduce a sort of curvature in the unit ball adapted to our kernel. We establish a good λ inequality which then yields the solution of this T(1)-type problem.
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[5] Hybrid mean value on the difference between an integer and its inverse modulo$q$
Huaning Liu Department of Mathematics, Northwest University Wenpeng Zhang Department of Mathematics, Northwest University
TBD mathscidoc:1701.333131
Arkiv for Matematik, 46, (2), 337-347, 2006.4
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[6] Time-global smoothing estimates for a class of dispersive equations with constant coefficients
Kei Morii Mathematical Institute, Tohoku University
TBD mathscidoc:1701.333132
Arkiv for Matematik, 46, (2), 363-375, 2006.12
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We discuss smoothing effects of homogeneous dispersive equations with constant coefficients. In the case where the characteristic root is positively homogeneous, time-global smoothing estimates are known. It is also known that a dispersiveness condition is necessary for smoothing effects. We show time-global smoothing estimates where the characteristic root is not necessarily homogeneous. Our results give a sufficient condition so that lower order terms can be absorbed by the principal part, and also indicate that smoothing effects may be caused by lower order terms in the case where the dispersiveness condition fails to hold.
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[7] A direct approach to Bergman kernel asymptotics for positive line bundles
Robert Berman Department of Mathematics, Chalmers University of Technology Bo Berndtsson Department of Mathematics, Chalmers University of Technology Johannes Sjöstrand Centre de Mathématiques Laurent Schwartz, Ecole Polytechnique
TBD mathscidoc:1701.333133
Arkiv for Matematik, 46, (2), 197-217, 2005.9
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[8] Higher order Riesz transforms associated with Bessel operators
Jorge J. Betancor Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta Juan C. Fariña Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta Teresa Martinez Departamento de Matemáticas, Faculdad de Ciencias, Universidad Autónoma de Madrid Lourdes Rodríguez-Mesa Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta
TBD mathscidoc:1701.333134
Arkiv for Matematik, 46, (2), 219-250, 2006.11
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In this paper we investigate Riesz transforms$R$_{μ}^{($k$)}of order$k$≥1 related to the Bessel operator Δ_{μ}$f$($x$)=-$f$”($x$)-((2μ+1)/$x$)$f$’($x$) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every$k$≥1,$R$_{μ}^{($k$)}is a principal value operator of strong type ($p$,$p$),$p$∈(1,∞), and weak type (1,1) with respect to the measure$d$λ($x$)=$x$^{2μ+1}$dx$in (0,∞). We also characterize the class of weights ω on (0,∞) for which$R$_{μ}^{($k$)}maps$L$^{$p$}(ω) into itself and$L$^{1}(ω) into$L$^{1,∞}(ω) boundedly. This class of weights is wider than the Muckenhoupt class $\mathcal{A}_{p}^\mu$ of weights for the doubling measure$d$λ. These weighted results extend the ones obtained by Andersen and Kerman.
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[9] Embeddings through discrete sets of balls
Stefan Borell Institute of Mathematics, University of Berne Frank Kutzschebauch Institute of Mathematics, University of Berne
TBD mathscidoc:1701.333135
Arkiv for Matematik, 46, (2), 251-269, 2006.12
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We investigate whether a Stein manifold$M$which allows proper holomorphic embedding into ℂ^{$n$}can be embedded in such a way that the image contains a given discrete set of points and in addition follow arbitrarily close to prescribed tangent directions in a neighbourhood of the discrete set. The infinitesimal version was proven by Forstnerič to be always possible. We give a general positive answer if the dimension of$M$is smaller than$n$/2 and construct counterexamples for all other dimensional relations. The obstruction we use in these examples is a certain hyperbolicity condition.
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[10] A Wiener–Wintner theorem for the Hilbert transform
Michael Lacey School of Mathematics, Georgia Institute of Technology Erin Terwilleger Department of Mathematics, U-3009, University of Connecticut
TBD mathscidoc:1701.333136
Arkiv for Matematik, 46, (2), 315-336, 2005.12
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We prove the following extension of the Wiener–Wintner theorem and the Carleson theorem on pointwise convergence of Fourier series: For all measure-preserving flows ($X$,μ,$T$_{$t$}) and$f$∈$L$^{$p$}($X$,μ), there is a set$X$_{$f$}⊂$X$of probability one, so that for all$x$∈$X$_{$f$}, $$\lim_{s\downarrow0}\int_{s<|t|<1/s}e^{i\theta t} f(\textup{T}_tx)\,\frac{dt}t\quad\text{exists for all}\ \theta.$$ The proof is by way of establishing an appropriate oscillation inequality which is itself an extension of Carleson’s theorem.
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Impact Factor
0.744
Available
1949 - 2016
Volumes
60
Issues
119
Articles
1382