Mathematische Nachrichten (Math Nachr)

Publications in this journal

• Article: Some s‐numbers of embeddings of function spaces with weights of logarithmic type

  Alicja Gąsiorowska, Leszek Skrzypczak
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  ABSTRACT: In this paper we deal with compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type with weights of logarithmic growth near infinity. We obtain the exact estimates for the asymptotic behaviour of Gelfand, Kolmogorov and Weyl numbers of the embeddings. As an application we get eigenvalue estimates of some degenerate pseudodifferential operators of type. Finally we deal with the “negative spectrum” of operators Hγ = A − γV for γ → ∞, where the potential V is a positive function and A is a positive elliptic pseudodifferential operator. We concentrate on the case when the Weyl numbers and Pietsch's inequality give us better estimates then entropy numbers and Carl's inequality.
  Mathematische Nachrichten 03/2012;
• Article: Global analytic, Gevrey and C∞ hypoellipticity on the 3‐torus

  A. Alexandrou Himonas, Gerson Petronilho, L. A. Carvalho dos Santos
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  ABSTRACT: It is proved that a class of sub-Laplacians on the 3-dimensional torus is globally analytic, Gevrey and C∞ hypoelliptic if and only if either a Diophantine condition holds or there is a point of finite type for the vector fields defining the operator under consideration. This work is motivated by the desire of attaining a better understanding of necessary and sufficient conditions for the global Gevrey and C∞ hypoellipticity of a sub-Laplacian on a compact analytic manifold. This together with the more delicate local hypoellipticity are well-known open problems in the theory of linear partial differential equations.
  Mathematische Nachrichten 01/2012; 285(2‐3):265 - 282.
• Article: Sheaves of slice regular functions

  Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa
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  ABSTRACT: Slice regular functions have been introduced in 20 as solutions of a special partial differential operator with variable coefficients. As such they do not naturally form a sheaf. In this paper we use a modified definition of slice regularity, see 21, to introduce the sheaf of slice regular functions with values in in the algebra of quaternions and, more in general, in a Clifford algebra and we study its cohomological properties. We show that the first cohomology group with coefficients in the sheaf of slice regular functions vanishes for any open set in the space of quaternions (resp. the space of paravectors in ). However, we prove that not all the open sets are domains of slice regularity but only those special sets which are axially symmetric, i.e., invariant with respect to rotations that fix the real axis.
  Mathematische Nachrichten 01/2012; 285(8‐9):949 - 958.
• Article: Sur l'allure des fonctions harmoniques et sousharmoniques à la frontière. En hommage de reconnaissance au professeur Erhard Schmidt.

  Par Marcel Brelot
  Mathematische Nachrichten 01/2012; 4(1):298 - 307.
• Article: Über den Hilbertschen Irreduzibilitätssatz. Erhard Schmidt zum 75. Geburtstag gewidmet

  GÜNther Preuss, Friedrich Karl Schmidt
  Mathematische Nachrichten 01/2012; 4(1):348 - 365.
• Article: On algebraic equations with all but one root in the interior of the unit circle. To my teacher and former colleague Erhard Schmidt on his 75th birthday

  Alfred Brauer
  Mathematische Nachrichten 01/2012; 4(1):250 - 257.
• Article: Die Überführung des Randwertproblems für Systeme elliptischer Differentialgleichungen auf Fredholmsche Integralgleichungen. I. Herrn Professor Dr. Erhard Schmidt zum 75. Geburtstag gewidmet

  Wolfgang Haack, GÜNter Hellwig
  Mathematische Nachrichten 01/2012; 4(1):408 - 418.
• Article: Beziehungen zwischen Klassenzahlen von Teilkörpern eines galoisschen Körpers. Herrn Professor Dr. Erhard Schmidt in dankbarer Verehrung zum 75. Geburtstag

  Richard Brauer
  Mathematische Nachrichten 01/2012; 4(1):158 - 174.
• Article: Über die Eigenwertaufgaben mit reellen diskreten Eigenwerten. Erhard Schmidt zum 75. Geburtstag gewidmet

  Helmut Wielandt
  Mathematische Nachrichten 01/2012; 4(1):308 - 314.
• Article: Analytische Mannigfaltigkeiten im komplexen projektiven Raum. Herrn Erhard Schmidt zum 75. Geburtstag gewidmet

  Hellmuth Kneser
  Mathematische Nachrichten 01/2012; 4(1):382 - 391.
• Article: Über Flächen mit einer Relation zwischen den Hauptkrümmungen. Meinem Lehrer Erhard Schmidt in Verehrung und Freundschaft zum 75. Geburtstag gewidmet.

  Heinz Hopf
  Mathematische Nachrichten 01/2012; 4(1):232 - 249.
• Article: Besov space and trace theorem on a local field and its application

  Hiroshi Kaneko
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  ABSTRACT: Recently, importance of the Besov space has been acknowledged by analysts studing such subsets with lower dimension than the whole space as fractals in the Euclidean space. On the other hand, by taking an extension K of local field K′, K′ is contained in K as a subset with lower dimension than the whole space K and the present author showed that it can be viewed as a d-set of K in terms of fractal analysis. In this article, Besov spaces on separable extension of the field of p-adic numbers and on its d-set will be consistently introduced. After that, a trace theorem showing a relationship between those Besov spaces will be presented and finally a penetrating stochastic process into K′ will be addressed as an application of the trace theorem.
  Mathematische Nachrichten 01/2012; 285(8‐9):981 - 996.
• Article: Gorenstein projective and flat complexes over noetherian rings

  Edgar Enochs, Sergio Estrada, Alina Iacob
  Mathematische Nachrichten 01/2012; 285(7):834-851.
• Article: Composition with distributions of Wiener‐Poisson variables and its asymptotic expansion

  Masafumi Hayashi, Yasushi Ishikawa
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  ABSTRACT: In this paper, we introduce the compositions of smooth Wiener-Poisson functional and Schwartz distribution by using Malliavin calculus jump type. We also prove Watanabe's theorem in the jump-diffusion case, that is, the asymptotic expansion formula for the compositions of a smooth Wiener-Poisson functional with Schwartz distributions.
  Mathematische Nachrichten 12/2011; 285(5‐6):619 - 658.
• Article: Character formulas for restricted simple modules of the special superalgebras

  Bin Shu, Yu-Feng Yao
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  ABSTRACT: Let k be an algebraically closed field of prime characteristic p > 2, and let S(n) be the special Lie superalgebra over k. The iso-classes of simple restricted modules of these algebras are classified, and the character formulas of restricted simple modules are given.
  Mathematische Nachrichten 12/2011; 285(8‐9):1107 - 1116.
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  Available from: wias-berlin.de

  Article: Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction‐diffusion systems

  Annegret Glitzky
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  ABSTRACT: Our focus are energy estimates for discretized reaction-diffusion systems for a finite number of species. We introduce a discretization scheme (Voronoi finite volume in space and fully implicit in time) which has the special property that it preserves the main features of the continuous systems, namely positivity, dissipativity and flux conservation.For a class of Voronoi finite volume meshes we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the discrete free energy to its equilibrium value with a unified rate of decay for this class of discretizations. The fundamental idea is an estimate of the free energy by the dissipation rate which is proved indirectly by taking into account sequences of Voronoi finite volume meshes. Essential ingredient in that proof is a discrete Sobolev-Poincaré inequality.
  Mathematische Nachrichten 11/2011; 284(17‐18):2159 - 2174.