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Subordinated Multiparameter Groups of Linear Operators: Properties via the Transference Principle

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Functional Analysis and Evolution Equations

Abstract

In this article we explore properties of subordinated d-parameter groups. We show that they are semi-groups, inheriting the properties of the subordinator via a transference principle. Applications range from infinitely divisible processes on a torus to the definition of inhomogeneous d-dimensional fractional derivative operators.

M. Kovács is partially supported by postdoctoral grant No. 623-2005-5078 of the Swedish Research Council and research grant (CZN-14/2005) of the Science and Technology Foundation.

M.M. Meerschaert is partially supported by USA National Science Foundation grant DMS-0417869.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Otago, Dunedin, New Zealand

    Boris Baeumer & Mihály Kovács

  2. Department of Statistics & Probability, Michigan State University, A413 Wells Hall, East Lansing, MI, 48824-1027, USA

    Mark M. Meerschaert

Authors
  1. Boris Baeumer
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  2. Mihály Kovács
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  3. Mark M. Meerschaert
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Herbert Amann

  2. Abteilung Angewandte Analysis, Universität Ulm, 89069, Ulm, Germany

    Wolfgang Arendt

  3. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, 64289, Darmstadt, Germany

    Matthias Hieber

  4. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Frank M. Neubrander

  5. Université de Valenciennes et du Hainaut Cambrésis, Le Mont Houy, 59313, Valenciennes Cedex 9, France

    Serge Nicaise

  6. Laboratoire de Mathématiques Pures et Appliquées — LMPA “Joseph Liouville”, Université du Littoral-Côte d’Opale, 50, rue F. Buisson, 62228, Calais Cedex, France

    Joachim von Below

Additional information

Dedicated to Günter Lumer; You were quite an inspiration!

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Baeumer, B., Kovács, M., Meerschaert, M.M. (2007). Subordinated Multiparameter Groups of Linear Operators: Properties via the Transference Principle. In: Amann, H., Arendt, W., Hieber, M., Neubrander, F.M., Nicaise, S., von Below, J. (eds) Functional Analysis and Evolution Equations. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7794-6_3

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