
New Developments in Pseudo-Differential Operators
ISAAC Group in Pseudo-Differential Operators (IGPDO), Middle East Technical University, Ankara,Turkey, August 2007
Birkhäuser (Publisher)
Published on 18. November 2008
Book
Hardback
VIII, 332 pages
978-3-7643-8968-0 (ISBN)
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.
Primary 47F30; Secondary 35B65, 46F05. Keywords. Degenerate elliptic operators, hypoellipticity, phase space Weyl calculus, Shubin symbols.
More details
Series
Edition
2009 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
VIII, 332 p.
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 25 mm
Weight
776 gr
ISBN-13
978-3-7643-8968-0 (9783764389680)
DOI
10.1007/978-3-7643-8969-7
Schweitzer Classification
Other editions
Additional editions

Luigi Rodino | M. W. Wong
New Developments in Pseudo-Differential Operators
ISAAC Group in Pseudo-Differential Operators (IGPDO), Middle East Technical University, Ankara,Turkey, August 2007
E-Book
01/2009
1st Edition
Birkhäuser
€96.29
Available for download
Content
Phase-Space Weyl Calculus and Global Hypoellipticity of a Class of Degenerate Elliptic Partial Differential Operators.- Classes of Degenerate Elliptic Operators in Gelfand-Shilov Spaces.- Weyl Transforms and the Heat Equation for the Sub-Laplacian on the Heisenberg Group.- Construction of the Fundamental Solution and Curvature of Manifolds with Boundary.- Operators with Corner-Degenerate Symbols.- Ellipticity of Fredholm Pseudo-Differential Operators on L p (? n ).- Hyperbolic Systems with Discontinuous Coefficients: Generalized Wavefront Sets.- Generalized Fourier Integral Operators on Spaces of Colombeau Type.- On Local and Global Regularity of Fourier Integral Operators.- Type 1,1-Operators Defined by Vanishing Frequency Modulation.- Regularity for Quasi-Elliptic Pseudo-Differential Operators with Symbols in Hölder Classes.- Multi-Anisotropic Gevrey Regularity of Hypoelliptic Operators.- Modified Stockwell Transforms and Time-Frequency Analysis.- Localization Operators for Two-Dimensional Stockwell Transforms.- Pseudo-Differential Operators on .- On Pseudo-Differential Operators on Group SU(2).- Sampling and Pseudo-Differential Operators.