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

New Developments in Pseudo-Differential Operators

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

By: Luigi Rodino (Editor), M. W. Wong (Editor)

Hardcover | 18 November 2008

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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."

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Non-FictionMathematicsCalculus & Mathematical AnalysisFunctional Analysis & TransformsDifferential Calculus & Equations

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