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Global Regularity and Stability in S-Spaces for Classes of Degenerate Shubin Operators

  • Todor Gramchev
  • Stevan Pilipović
  • Luigi Rodino
Part of the Operator Theory: Advances and Applications book series (OT, volume 205)

Abstract

We study the uniform regularity and the decay at infinity for anisotropic tensor products of Shubin-type differenential operators as well as for degenerate harmonic oscillators. As applications of our general results we obtain new theorems for global hypoellipticity for classes of degenerate operators in inductive and projective Gelfand-Shilov spaces.

Keywords

S-spaces Shubin-type pseudo-differential operators Gelfand-Shilov spaces 

Methematics Subject Classification (2000)

Primary 47F30 Secondary 46F05 35B65 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Todor Gramchev
    • 1
  • Stevan Pilipović
    • 2
  • Luigi Rodino
    • 3
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly
  2. 2.Institute of MathematicsUniversity of Novi SadTrg D. Obradovića 4Novi SadSerbia
  3. 3.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

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