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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 (Hardcover, 2009 ed.)
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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 (Hardcover, 2009 ed.)
Series: Operator Theory: Advances and Applications, 189
Expected to ship within 10 - 15 working days
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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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