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Arkiv for Matematik, 2001
ISSN:
0004-2080 (Print)
1871-2487 (Online)
In this year (20 articles)
Volume 40, Issue 1
[1] Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture
Christopher J. Bishop Mathematics Department, State University of New York at Stony Brook
TBD mathscidoc:1701.332971
Arkiv for Matematik, 40, (1), 1-26, 2000.10
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We show that proving the conjectured sharp constant in a theorem of Dennis Sullivan concerning convex sets in hyperbolic 3-space would imply the Brennan conjecture. We also prove that any conformal map$f$:$D$→Ω can be factored as a$K$-quasiconformal self-map of the disk (with$K$independent of Ω) and a map$g$:$D$→Ω with derivative bounded away from zero. In particular, there is always a Lipschitz homeomorphism from any simply connected Ω (with its internal path metric) to the unit disk.
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[2] Maximal plurisubharmonic functions and the polynomial hull of a completely circled fibration
Miran Černe Department of Mathematics, University of Ljubljana
TBD mathscidoc:1701.332972
Arkiv for Matematik, 40, (1), 27-45, 2000.4
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Let$X$(-ϱ$B$^{$m$}×$C$^{$n$}be a compact set over the unit sphere ϱ$B$^{$m$}such that for each$z$∈ϱ$B$^{$m$}the fiber$X$_{$z$}={ω∈$C$^{$n$};($z, ω$)∈$X$} is the closure of a completely circled pseudoconvex domain in$C$^{$n$}. The polynomial hull $$\hat X$$ of$X$is described in terms of the Perron-Bremermann function for the homogeneous defining function of$X$. Moreover, for each point ($z$_{0},$w$_{0})∈Int $$\hat X$$ there exists a smooth up to the boundary analytic disc$F$:Δ→$B$^{$m$}×$C$^{$n$}with the boundary in$X$such that$F$(0)=($z$_{0},$w$_{0}).
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[3] A remark on local-global principles for conjugacy classes
Yuval Z. Flicker Department of Mathematics, Ohio State University
TBD mathscidoc:1701.332973
Arkiv for Matematik, 40, (1), 47-53, 2000.9
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A local-global principle is shown to hold for all conjugacy classes of any inner form of GL($n$), SL($n$), U($n$), SU($n$), and for all semisimple conjugacy classes in any inner form of Sp($n$), over fields$k$with vcd($k$)≤1. Over number fields such a principle is known to hold for any inner form of GL($n$) and U($n$), and for the split forms of Sp($n$), O($n$), as well as for SL($p$) but not for SL($n$),$n$non-prime. The principle holds for all conjugacy classes in any inner form of GL($n$), but not even for semisimple conjugacy classes in Sp($n$), over fields$k$with vcd($k$)≤2. The principle for conjugacy classes is related to that for centralizers.
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[4] On the Titchmarsh convolution theorem
Seçil Gergün Department of Mathematics, Bilkent University Iossif V. Ostrovskii Department of Mathematics, Bilkent University Alexander Ulanovskii Høgskolen i Stavanger, P.O. Box 2557, Ullandhaug, Stavanger, Norway
TBD mathscidoc:1701.332974
Arkiv for Matematik, 40, (1), 55-71, 2000.5
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[5] On the number of bound states for Schrödinger operators with operator-valued potentials
Dirk Hundertmark Department of Mathematics 253-37, California Institute of Technology
TBD mathscidoc:1701.332975
Arkiv for Matematik, 40, (1), 73-87, 2000.11
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Cwikel's bound is extended to an operator-valued setting. One application of this result is a semi-classical bound for the number of negative bound states for Schrödinger operators with operator-valued potentials. We recover Cwikel's bound for the Lieb-Thirring constant$L$_{0,3}which is far worse than the best available by Lieb (for scalar potentials). However, it leads to a uniform bound (in the dimension$d$≥3) for the quotient$L$_{0,d}/L^{cl}_{0,d}is the so-called classical constant. This gives some improvement in large dimensions.
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[6] The harmonic Bergman kernel and the Friedrichs operator
Stefan Jakobsson Centre for Mathematical Sciences, Lund University
TBD mathscidoc:1701.332976
Arkiv for Matematik, 40, (1), 89-104, 2000.9
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The harmonic Bergman kernel$Q$_{Ω}for a simply, connected planar domain Ω can be expanded in terms of powers of the Friedrichs operator$F$_{Ω}║$F$_{Ω}║<1 in operator norm. Suppose that Ω is the image of a univalent analytic function ø in the unit disk with ø' ($z$)=1+ψ ($z$) where ψ(0)=0. We show that if the function ψ belongs to a space$D$_{$s$}($D$),$s$>0, of Dirichlet type, then provided that ║ψ║∞<1 the series for$Q$_{Ω}also converges pointwise in $$\bar \Omega \times \bar \Omega \backslash \Delta (\partial \Omega )$$ , and the rate of convergence can be estimated. The proof uses the eigenfunctions of the Friedrichs operator as well as a formula due to Lenard on projections in Hilbert spaces. As an application, we show that for every$s$>0 there exists a constant$C$_{$s$}>0 such that if ║ψ║_{$D$}_{s}($D$)≤$C$_{$s$}, then the biharmonic Green function for Ω=ø ($D$) is positive.
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[7] Very weak solutions of parabolic systems of$p$-Laplacian type
Juha Kinnunen Institute of Mathematics, Helsinki University of Technology John L. Lewis Department of Mathematics, University of Kentucky
TBD mathscidoc:1701.332977
Arkiv for Matematik, 40, (1), 105-132, 2000.12
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[8] $L$^{$p$}-norms of Hermite polynomials and an extremal problem on Wiener chaos
Lars Larsson-Cohn Department of Mathematics, Uppsala University
TBD mathscidoc:1701.332978
Arkiv for Matematik, 40, (1), 133-144, 2000.10
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[9] An inversion formula for the attenuated X-ray transformation
Roman G. Novikov CNRS, UMR 6629 Département de Mathématiques, Université de Nantes
TBD mathscidoc:1701.332979
Arkiv for Matematik, 40, (1), 145-167, 2000.5
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[10] Gabor analysis of the continuum model for impedance tomography
Victor P. Palamodov School of Mathematical Sciences, Tel Aviv University
TBD mathscidoc:1701.332980
Arkiv for Matematik, 40, (1), 169-187, 2000.7
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[11] Resultants and the Hilbert scheme of points on the line
Roy Mikael Skjelnes Department of Mathematics, Royal Institute of Technology
TBD mathscidoc:1701.332981
Arkiv for Matematik, 40, (1), 189-200, 2000.11
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We present an elementary and concrete description of the Hilbert scheme of points on the spectrum of fraction rings$k[X]$_{$U$}of the one-variable polynomial ring over a commutative ring$k$. Our description is based on the computation of the resultant of polynomials in$k[X]$. The present paper generalizes the results of Laksov-Skjelnes [7], where the Hilbert scheme on spectrum of the local ring of a point was described.
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[12] A non-existence theorem of lacunas for hyperbolic differential operators with constant coefficients
Motoo Uchida Department of Mathematics Graduate School of Science, Osaka University
TBD mathscidoc:1701.332982
Arkiv for Matematik, 40, (1), 201-205, 2000.12
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Volume 40, Issue 2
[1] Dynamics of polynomial automorphisms of$C$^{$k$}
Vincent Guedj Laboratoire Emile Picard UMR 5580, Université Paul Sabatier Nessim Sibony Mathémathiques, Université Paris-Sud
TBD mathscidoc:1701.332983
Arkiv for Matematik, 40, (2), 207-243, 2001.4
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We study the dynamics of polynomial automorphisms of$C$^{$k$}. To an algebraically stable automorphism we associate positive closed currents which are invariant under$f$, considering$f$as a rational map on$P$^{$k$}. These currents give information on the dynamics and allow us to construct a canonical invariant measure which is shown to be mixing.
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[2] Approximation in Sobolev spaces of nonlinear expressions involving the gradient
Piotr Hajłasz Institute of Mathematics, Warsaw University Jan Malý Department of Mathematical Analysis, Charles University
TBD mathscidoc:1701.332984
Arkiv for Matematik, 40, (2), 245-274, 2001.2
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We investigate a problem of approximation of a large class of nonlinear expressions$f$($x, u$, ∇$u$), including polyconvex functions. Here$u$: Ω→$R$^{$m$}, Ω⊂$R$^{$n$}, is a mapping from the Sobolev space$W$^{$1,p$}. In particular, when$p=n$, we obtain the approximation by mappings which are continuous, differentiable a.e. and, if in addition$n=m$, satisfy the Luzin condition. From the point of view of applications such mappings are almost as good as Lipschitz mappings. As far as we know, for the nonlinear problems that we consider, no natural approximation results were known so far. The results about the approximation of$f$($x, u$, ∇$u$) are consequences of the main result of the paper, Theorem 1.3, on a very strong approximation of Sobolev functions by locally weakly monotone functions.
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[3] Interior regularity of solutions to a complex Monge-Ampère equation
Björn Ivarsson Department of Mathematics, Uppsala University
TBD mathscidoc:1701.332985
Arkiv for Matematik, 40, (2), 275-300, 2001.1
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We give interior estimates for first derivatives of solutions to a type of complex Monge-Ampère equations in convex domains. We also show global estimates for first derivatives of solutions in arbitrary domains. These global estimates are then used to show interior regularity of solutions to the complex Monge-Ampère equations in hyperconvex domains having a bounded exhaustion function which is globally Lipschitz. Finally we give examples of domains which have such an exhaustion function and domains which do not.
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[4] A separation theorem and Serre duality for the Dolbeault cohomology
Christine Laurent-Thiébaut UMR 5582 CNRS-UJF Institut Fourier, Université Grenoble I Jürgen Leiterer Institut für Mathematik, Humboldt-Universität zu Berlin
TBD mathscidoc:1701.332986
Arkiv for Matematik, 40, (2), 301-321, 2000.5
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Let$X$be a complex manifold with finitely many ends such that each end is either$q$-concave or ($n−q$)-convex. If $$q< \tfrac{1}{2}n$$ , then we prove that$H$^{p$n−q$}$(X)$is Hausdorff for all$p$. This is not true in general if $$q \geqslant \tfrac{1}{2}n$$ (Rossi’s example with$n$=2 and$q$=1). If all ends are$q$-concave, then this is the classical Andreotti-Vesentini separation theorem (and holds also for $$q \geqslant \tfrac{1}{2}n$$ ). Moreover the result was already known in the case when the$q$-concave ends can be ‘filled in’ (again also for $$q \geqslant \tfrac{1}{2}n$$ ). To prove the result we first have to study Serre duality for the case of more general families of supports (instead of the family of all closed sets and the family of all compact sets) which is the main part of the paper. At the end we give an application to the extensibility of CR-forms of bidegree ($p, q$) from ($n−q$)-convex boundaries, $$q< \tfrac{1}{2}n$$ .
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[5] On$M$-structure, the asymptotic-norming property and locally uniformly rotund renormings
Eduardo Nieto Departamento de Análisis Matemático Facultad de Ciencias, Universidad de Granada Migdalia Rivas Departamento de Análisis Matemático Facultad de Ciencias, Universidad de Granada
TBD mathscidoc:1701.332987
Arkiv for Matematik, 40, (2), 323-333, 2000.8
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Let$r, s$∈ [0, 1], and let$X$be a Banach space satisfying the$M(r, s)$-inequality, that is, $$\parallel x^{***} \parallel \geqslant r\parallel \pi _X x^{***} \parallel + s\parallel x^{***} - \pi _X x^{***} \parallel for x^{***} \in X^{***} ,$$ where π_{$X$}is the canonical projection from$X$^{***}onto$X$^{*}. We show some examples of Banach spaces not containing$c$_{0}, having the point of continuity property and satisfying the above inequality for$r$not necessarily equal to one. On the other hand, we prove that a Banach space$X$satisfying the above inequality for$s$=1 admits an equivalent locally uniformly rotund norm whose dual norm is also locally uniformly rotund. If, in addition,$X$satisfies $$\mathop {\lim \sup }\limits_\alpha \parallel u^* + sx_\alpha ^* \parallel \leqslant \mathop {\lim \sup }\limits_\alpha \parallel v^* + x_\alpha ^* \parallel $$ whenever$u$^{*},$v$^{*}∈$X$^{*}with ‖$u$^{*}‖≤‖$v$^{*}‖ and ($x$_{α}^{*}) is a bounded weak^{*}null net in$X$^{*}, then$X$can be renormed to satisfy the,$M(r, 1)$and the$M(1, s)$-inequality such that$X$^{*}has the weak^{*}asymptotic-norming property I with respect to$B$_{$X$}.
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[6] Level sets of harmonic functions on the Sierpiński gasket
Anders Öberg Department of Mathematics, Uppsala University Robert S. Strichartz Mathematics Department Malott Hall, Cornell University Andrew Q. Yingst Mathematics Department, University of North Texas
TBD mathscidoc:1701.332988
Arkiv for Matematik, 40, (2), 335-362, 2001.6
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We give a detailed description of nonconstant harmonic functions and their level sets on the Sierpiński gasket. We introduce a parameter, called$eccentricity$, which classifies these functions up to affine transformations$h→ah+b$. We describe three (presumably) distinct measures that describe how the eccentricities are distributed in the limit as we subdivide the gasket into smaller copies (cells) and restrict the harmonic function to the small cells. One measure simply counts the number of small cells with eccentricity in a specified range. One counts the contribution to the total energy coming from those cells. And one counts just those cells that intersect a fixed generic level set. The last measure yields a formula for the box dimension of a generic level set. All three measures are defined by invariance equations with respect to the same iterated function system, but with different weights. We also give a construction for a rectifiable curve containing a given level set. We exhibit examples where the curve has infinite winding number with respect to some points.
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[7] Sobolev spaces in several variables in$L$^{1}-type norms are not isomorphic to Banach lattices
Aleksander Pełczyński Institute of Mathematics, Polish Academy of Sciences Michał Wojciechowski Institute of Mathematics, Polish Academy of Sciences
TBD mathscidoc:1701.332989
Arkiv for Matematik, 40, (2), 363-382, 2001.5
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[8] Decomposition theorems for$Q$_{$p$}spaces
Zhijian Wu Department of Mathematics, University of Alabama Chunping Xie Department of Mathematics, University of Alabama
TBD mathscidoc:1701.332990
Arkiv for Matematik, 40, (2), 383-401, 2001.4
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We study the Möbius invariant spaces$Q$_{$p$}and$Q$_{$p, 0$}of analytic functions. These scales of spaces include BMOA=$Q$_{1}, VMOA=$Q$_{1, 0}and the Dirichlet space=$Q$_{0}. Using the Bergman metric, we establish decomposition theorems for these spaces. We obtain also a fractional derivative characterization for both$Q$_{$p$}and$Q$_{$p, 0$}.
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Impact Factor
0.744
Available
1949 - 2016
Volumes
60
Issues
119
Articles
1382