New Developments in Pseudo-Differential Operators : ISAAC Group in Pseudo-Differential Operators (IGPDO), Middle East Technical University, Ankara,Turkey, August 2007, Hardback Book

New Developments in Pseudo-Differential Operators : ISAAC Group in Pseudo-Differential Operators (IGPDO), Middle East Technical University, Ankara,Turkey, August 2007 Hardback

Edited by Luigi Rodino, M. W. Wong

Part of the Operator Theory: Advances and Applications series

Description

di?erential operators in particular will be developed hand in glove with appli- tions andcomputation inthe physical,biologicaland medicalsciences.This theme will play an important role in the forthcoming volumes on pseudo-di?erential - erators originating from IGPDO.

The Editors OperatorTheory: Advances andApplications,Vol.189, 1-14 c 2008Birkh. auserVerlagBasel/Switzerland Phase-Space Weyl Calculus and Global Hypoellipticity of a Class of Degenerate Elliptic Partial Di?erential Operators Maurice de Gosson Abstract.

In a recent series of papers M.W. Wong has studied a degenerate elliptic partial di?erential operator related to the Heisenberg group.

It turns out that Wong's example is best understood when replaced in the context of the phase-space Weyl calculus we have developed in previous work; this - proach highlights the relationship of Wong's constructions with the quantum mechanics of charged particles in a uniform magnetic ?eld.

Using Shubin's classes of pseudodi?erential symbols we prove global hypoellipticity results for arbitrary phase-space operators arising from elliptic operators on con- uration space.

Mathematics Subject Classi?cation (2000). Primary 47F30; Secondary 35B65, 46F05. Keywords. Degenerate elliptic operators, hypoellipticity, phase space Weyl calculus, Shubin symbols.

Information

  • Format: Hardback
  • Pages: 332 pages, VIII, 332 p.
  • Publisher: Birkhauser Verlag AG
  • Publication Date:
  • Category: Differential calculus & equations
  • ISBN: 9783764389680

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