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
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.
- Format: Hardback
- Pages: 332 pages, VIII, 332 p.
- Publisher: Birkhauser Verlag AG
- Publication Date: 18/11/2008
- Category: Differential calculus & equations
- ISBN: 9783764389680