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Arkiv for Matematik, 2009, Volume 48
ISSN:
0004-2080 (Print)
1871-2487 (Online)
In this volume (23 articles)
Issue 1
[1] A residue criterion for strong holomorphicity
Mats Andersson Department of Mathematics, Chalmers University of Technology
TBD mathscidoc:1701.333156
Arkiv for Matematik, 48, (1), 1-15, 2008.1
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[2] Transfinite diameter notions in ℂ^{$N$}and integrals of Vandermonde determinants
Thomas Bloom University of Toronto, Toronto, Ontario, Canada Norman Levenberg Indiana University, Bloomington, IN, U.S.A.
TBD mathscidoc:1701.333157
Arkiv for Matematik, 48, (1), 17-40, 2008.2
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We provide a general framework and indicate relations between the notions of transfinite diameter, homogeneous transfinite diameter, and weighted transfinite diameter for sets in ℂ^{$N$}. An ingredient is a formula of Rumely (A Robin formula for the Fekete–Leja transfinite diameter,$Math. Ann.$$337$(2007), 729–738) which relates the Robin function and the transfinite diameter of a compact set. We also prove limiting formulas for integrals of generalized Vandermonde determinants with varying weights for a general class of compact sets and measures in ℂ^{$N$}. Our results extend to certain weights and measures defined on cones in ℝ^{$N$}.
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[3] Spherical spectral synthesis and two-radius theorems on Damek–Ricci spaces
Norbert Peyerimhoff Department of Mathematical Sciences, University of Durham Evangelia Samiou Department of Mathematics and Statistics, University of Cyprus
TBD mathscidoc:1701.333158
Arkiv for Matematik, 48, (1), 131-147, 2008.4
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[4] Smooth tropical surfaces with infinitely many tropical lines
Magnus Dehli Vigeland Department of Mathematics, University of Oslo
TBD mathscidoc:1701.333159
Arkiv for Matematik, 48, (1), 177-206, 2008.1
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We study the tropical lines contained in smooth tropical surfaces in ℝ^{3}. On smooth tropical quadric surfaces we find two one-dimensional families of tropical lines, like in classical algebraic geometry. Unlike the classical case, however, there exist smooth tropical surfaces of any degree with infinitely many tropical lines.
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[5] A long ℂ^{2}which is not Stein
Erlend Fornæss Wold Department of Mathematics, University of Oslo
TBD mathscidoc:1701.333160
Arkiv for Matematik, 48, (1), 207-210, 2007.11
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[6] General Hausdorff functions, and the notion of one-sided measure and dimension
Claude Tricot Département de Mathématiques, Université Clermont-Ferrand II
TBD mathscidoc:1701.333161
Arkiv for Matematik, 48, (1), 149-176, 2008.1
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The main facts about Hausdorff and packing measures and dimensions of a Borel set$E$are revisited, using$determining$set functions $\phi_\alpha\colon\mathcal{B}_E\to(0,\infty)$ , where $\mathcal{B}_E$ is the family of all balls centred on$E$and α is a real parameter. With mild assumptions on φ_{α}, we verify that the main density results hold, as well as the basic properties of the corresponding box dimension. Given a bounded open set$V$in ℝ^{$D$}, these notions are used to introduce the$interior$and$exterior$measures and dimensions of any Borel subset of ∂$V$. We stress that these dimensions depend on the choice of φ_{α}. Two determining functions are considered, φ_{α}($B$)=Vol_{$D$}($B$∩$V$)diam($B$)^{α-$D$}and φ_{α}($B$)=Vol_{$D$}($B$∩$V$)^{α/$D$}, where Vol_{$D$}denotes the$D$-dimensional volume.
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[7] A multi-dimensional Markov chain and the Meixner ensemble
Kurt Johansson Department of Mathematics, Royal Institute of Technology
TBD mathscidoc:1701.333162
Arkiv for Matematik, 48, (1), 79-95, 2007.11
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We show that the transition probability of the Markov chain ($G$($i$,1),...,$G$($i$,$n$))_{$i$≥1}, where the$G$($i$,$j$)’s are certain directed last-passage times, is given by a determinant of a special form. An analogous formula has recently been obtained by Warren in a Brownian motion model. Furthermore we demonstrate that this formula leads to the Meixner ensemble when we compute the distribution function for$G$($m$,$n$). We also obtain the Fredholm determinant representation of this distribution, where the kernel has a double contour integral representation.
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[8] Equivariant Schubert calculus
Letterio Gatto Dipartimento di Matematica, Politecnico di Torino Taíse Santiago Instituto de Matemática, Universidade Federal da Bahia
TBD mathscidoc:1701.333163
Arkiv for Matematik, 48, (1), 41-55, 2008.1
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We describe$T$-equivariant Schubert calculus on$G$($k$,$n$),$T$being an$n$-dimensional torus, through derivations on the exterior algebra of a free$A$-module of rank$n$, where$A$is the$T$-equivariant cohomology of a point. In particular,$T$-equivariant Pieri’s formulas will be determined, answering a question raised by Lakshmibai, Raghavan and Sankaran (Equivariant Giambelli and determinantal restriction formulas for the Grassmannian,$Pure Appl. Math. Quart.$$2$(2006), 699–717).
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[9] Rigidity of the harmonic map heat flow from the sphere to compact Kähler manifolds
Qingyue Liu School of Mathematical Sciences, Peking University Yunyan Yang Department of Mathematics, Renmin University of China
TBD mathscidoc:1701.333164
Arkiv for Matematik, 48, (1), 121-130, 2008.2
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A Łojasiewicz-type estimate is a powerful tool in studying the rigidity properties of the harmonic map heat flow. Topping proved such an estimate using the Riesz potential method, and established various uniformity properties of the harmonic map heat flow from $\mathbb{S}^{2}$ to $\mathbb{S}^{2}$ ($J. Differential Geom.$$45$(1997), 593–610). In this note, using an inequality due to Sobolev, we will derive the same estimate for maps from $\mathbb{S}^{2}$ to a compact Kähler manifold$N$with nonnegative holomorphic bisectional curvature, and use it to establish the uniformity properties of the harmonic map heat flow from $\mathbb{S}^{2}$ to$N$, which generalizes Topping’s result.
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[10] A moment problem for pseudo-positive definite functionals
Ognyan Kounchev Institute of Mathematics and Informatics, Bulgarian Academy of Sciences Hermann Render School of Mathematical Sciences, University College Dublin
TBD mathscidoc:1701.333165
Arkiv for Matematik, 48, (1), 97-120, 2008.1
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[11] Matrix subspaces and determinantal hypersurfaces
Marko Huhtanen Institute of Mathematics, Helsinki University of Technology
TBD mathscidoc:1701.333166
Arkiv for Matematik, 48, (1), 57-77, 2008.4
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Nonsingular matrix subspaces can be separated into two categories: by being either invertible, or merely possessing invertible elements. The former class was introduced for factoring matrices into the product of two matrices. With the latter, the problem of characterizing the inverses and related nonlinear matrix geometries arises. For the singular elements there is a natural concept of spectrum defined in terms of determinantal hypersurfaces, linking matrix analysis with algebraic geometry. With this, matrix subspaces and the respective Grassmannians are split into equivalence classes. Conditioning of matrix subspaces is addressed.
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Issue 2
[1] The arithmetic-geometric scaling spectrum for continued fractions
Johannes Jaerisch Fachbereich Mathematik, Universität Bremen Marc Kesseböhmer Fachbereich Mathematik, Universität Bremen
TBD mathscidoc:1701.333167
Arkiv for Matematik, 48, (2), 335-360, 2009.2
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To compare continued fraction digits with the denominators of the corresponding approximants we introduce the arithmetic-geometric scaling. We will completely determine its multifractal spectrum by means of a number-theoretical free-energy function and show that the Hausdorff dimension of sets consisting of irrationals with the same scaling exponent coincides with the Legendre transform of this free-energy function. Furthermore, we identify the asymptotic of the local behaviour of the spectrum at the right boundary point and discuss a connection to the set of irrationals with continued-fraction digits exceeding a given number which tends to infinity.
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[2] Decomposition of$D$-modules over a hyperplane arrangement in the plane
Tilahun Abebaw Department of Mathematics, Addis Ababa University Rikard Bøgvad Department of Mathematics, Stockholm University
TBD mathscidoc:1701.333168
Arkiv for Matematik, 48, (2), 211-229, 2008.11
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Let$α$_{1},$α$_{2},…,$α$_{$m$}be linear forms defined on ℂ^{$n$}and $\mathcal{X}=\mathbb{C}^{n}\setminus\bigcup_{i=1}^{m}V(\alpha_{i})$ , where$V$($α$_{$i$})={$p$∈ℂ^{$n$}$:$$α$_{$i$}($p$)=0}. The coordinate ring $O_{\mathcal{X}}$ of $\mathcal{X}$ is a holonomic$A$_{$n$}-module, where$A$_{$n$}is the$n$th Weyl algebra and since holonomic$A$_{$n$}-modules have finite length, $O_{\mathcal{X}}$ has finite length. We consider a “twisted” variant of this$A$_{$n$}-module which is also holonomic. Define M_{$α$}^{$β$}to be the free rank-1 ℂ[$x$]_{$α$}-module on the generator$α$^{$β$}(thought of as a multivalued function), where $\alpha^{\beta}=\alpha_{1}^{\beta_{1}},\ldots,\alpha_{m}^{\beta_{m}}$ and the multi-index$β$=($β$_{1},…,$β$_{$m$})∈ℂ^{$m$}. Our main result is the computation of the number of decomposition factors of M_{$α$}^{$β$}and their description when$n$=2.
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[3] Quasi-parabolic analytic transformations of$C$^{$n$}. Parabolic manifolds
Feng Rong Department of Mathematics, Syracuse University
TBD mathscidoc:1701.333169
Arkiv for Matematik, 48, (2), 361-370, 2008.6
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In [$Rong$, F., Quasi-parabolic analytic transformations of$C$^{$n$},$J. Math. Anal. Appl.$$343$(2008), 99–109], we showed the existence of “parabolic curves” for certain quasi-parabolic analytic transformations of$C$^{$n$}. Under some extra assumptions, we show the existence of “parabolic manifolds” for such transformations.
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[4] Solvability of elliptic systems with square integrable boundary data
Pascal Auscher Université Paris-Sud 11 UMR 8628 du CNRS, Orsay Cedex, France Andreas Axelsson Department of Mathematics, Stockholm University Alan McIntosh Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University
TBD mathscidoc:1701.333170
Arkiv for Matematik, 48, (2), 253-287, 2008.10
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We consider second order elliptic divergence form systems with complex measurable coefficients$A$that are independent of the transversal coordinate, and prove that the set of$A$for which the boundary value problem with$L$_{2}Dirichlet or Neumann data is well posed, is an open set. Furthermore we prove that these boundary value problems are well posed when$A$is either Hermitean, block or constant. Our methods apply to more general systems of partial differential equations and as an example we prove perturbation results for boundary value problems for differential forms.
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[5] Maximal invariant subspaces for a class of operators
Kunyu Guo School of Mathematical Sciences, Fudan University Wei He Department of Mathematics, Southeast University Shengzhao Hou Department of Mathematics, Suzhou University
TBD mathscidoc:1701.333171
Arkiv for Matematik, 48, (2), 323-333, 2008.9
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In this note, we characterize maximal invariant subspaces for a class of operators. Let$T$be a Fredholm operator and $1-TT^{*}\in\mathcal{S}_{p}$ for some$p$≥1. It is shown that if$M$is an invariant subspace for$T$such that dim$M$$⊖$$TM$<∞, then every maximal invariant subspace of$M$is of codimension 1 in$M$. As an immediate consequence, we obtain that if$M$is a shift invariant subspace of the Bergman space and dim$M$$⊖$$zM$<∞, then every maximal invariant subspace of$M$is of codimension 1 in$M$. We also apply the result to translation operators and their invariant subspaces.
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[6] Finiteness results for lattices in certain Lie groups
Frederick P. Greenleaf Courant Institute of Mathematical Sciences, New York University Martin Moskowitz Ph.D. Program in Mathematics Graduate Center, City University of New York
TBD mathscidoc:1701.333172
Arkiv for Matematik, 48, (2), 311-321, 2008.6
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In this note we establish some general finiteness results concerning lattices Γ in connected Lie groups$G$which possess certain “density” properties (see$Moskowitz$, M., On the density theorems of Borel and Furstenberg,$Ark. Mat.$$16$(1978), 11–27, and$Moskowitz$, M., Some results on automorphisms of bounded displacement and bounded cocycles,$Monatsh. Math.$$85$(1978), 323–336). For such groups we show that Γ always has finite index in its normalizer$N$_{$G$}(Γ). We then investigate analogous questions for the automorphism group Aut($G$) proving, under appropriate conditions, that Stab_{Aut($G$)}(Γ) is discrete. Finally we show, under appropriate conditions, that the subgroup $\tilde{\Gamma}=\{i_{\gamma}:\gamma \in \Gamma \},\ i_{\gamma}(x)=\gamma x\gamma^{-1}$ , of Aut($G$) has finite index in Stab_{Aut($G$)}(Γ). We test the limits of our results with various examples and counterexamples.
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[7] On the completeness of certain kernel-defined semi-inner product spaces
Reinhard Wolf Fachbereich Mathematik, Universität Salzburg
TBD mathscidoc:1701.333173
Arkiv for Matematik, 48, (2), 395-403, 2009.1
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[8] A natural map in local cohomology
Moharram Aghapournahr Arak University, P.O. Box 879, Beheshti St, Arak, Iran Leif Melkersson Department of Mathematics, Linköping University
TBD mathscidoc:1701.333174
Arkiv for Matematik, 48, (2), 243-251, 2008.11
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Let$R$be a Noetherian ring, $\mathfrak{a}$ an ideal of$R$,$M$an$R$-module and$n$a non-negative integer. In this paper we first study the finiteness properties of the kernel and the cokernel of the natural map $f\colon\operatorname{Ext}^{n}_{R}(R/\mathfrak{a},M)\to \operatorname{Hom}_{R}(R/\mathfrak{a},\mathrm{H}^{n}_{\mathfrak{a}}(M))$ , under some conditions on the previous local cohomology modules. Then we get some corollaries about the associated primes and Artinianness of local cohomology modules. Finally we will study the asymptotic behavior of the kernel and the cokernel of the natural map in the graded case.
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[9] Riesz transform characterization of Hardy spaces associated with Schrödinger operators with compactly supported potentials
Jacek Dziubański Instytut Matematyczny, Uniwersytet Wrocławski Marcin Preisner Instytut Matematyczny, Uniwersytet Wrocławski
TBD mathscidoc:1701.333175
Arkiv for Matematik, 48, (2), 301-310, 2009.2
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Let$L$=−Δ+$V$be a Schrödinger operator on ℝ^{$d$},$d$≥3. We assume that$V$is a nonnegative, compactly supported potential that belongs to$L$^{$p$}(ℝ^{$d$}), for some$p$>$d$$/$2. Let$K$_{$t$}be the semigroup generated by −$L$. We say that an$L$^{1}(ℝ^{$d$})-function$f$belongs to the Hardy space $H^{1}_{L}$ associated with$L$if sup_{$t$>0}|$K$_{$t$}$f$| belongs to$L$^{1}(ℝ^{$d$}). We prove that $f\in H^{1}_{L}$ if and only if$R$_{$j$}$f$∈$L$^{1}(ℝ^{$d$}) for$j$=1,…,$d$, where$R$_{$j$}=($∂$/$∂$$x$_{$j$})$L$^{−1$/$2}are the Riesz transforms associated with$L$.
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[10] The hitting distributions of a half real line for two-dimensional random walks
Kôhei Uchiyama Department of Mathematics, Tokyo Institute of Technology
TBD mathscidoc:1701.333176
Arkiv for Matematik, 48, (2), 371-393, 2008.6
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For every two-dimensional random walk on the square lattice$Z$^{2}having zero mean and finite variance we obtain fine asymptotic estimates of the probability that the walk hits the negative real line for the first time at a site ($s$,0), when it is started at a site far from both (0,$s$) and the origin.
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[11] Some preserver problems on algebras of smooth functions
Félix Cabello Sánchez Departamento de Matemáticas, Universidad de Extremadura Javier Cabello Sánchez Departamento de Matemáticas, Universidad de Extremadura
TBD mathscidoc:1701.333177
Arkiv for Matematik, 48, (2), 289-300, 2008.9
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[12] On hypoellipticity of generators of Lévy processes
Helmut Abels Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, Leipzig, Germany Ryad Husseini Institute for Applied Mathematics, University of Bonn
TBD mathscidoc:1701.333178
Arkiv for Matematik, 48, (2), 231-242, 2008.8
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We give a sufficient condition on a Lévy measure$μ$which ensures that the generator$L$of the corresponding pure jump Lévy process is (locally) hypoelliptic, i.e., $\mathop {\mathrm {sing\,supp}}u\subseteq \mathop {\mathrm {sing\,supp}}Lu$ for all admissible$u$. In particular, we assume that $\mu|_{\mathbb {R}^{d}\setminus \{0\}}\in C^{\infty}(\mathbb {R}^{d}\setminus \{0\})$ . We also show that this condition is necessary provided that $\mathop {\mathrm {supp}}\mu$ is compact.
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Impact Factor
0.744
Available
1949 - 2016
Volumes
60
Issues
119
Articles
1382