Pseudo-differential operators : quantization and signals : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-24, 2006

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted. Banach Gelfand Triples For Gabor Analysis / H. Feichtinger, F. Luef, And E. Cordero -- Four Lectures In Semiclassical Analysis For Non Self-adjoint Problems With Applications To Hydrodynamic Instability / B. Helffer -- An Introduction To Numerical Methods Of Pseudodifferential Operators / M.p. Lamoureux And F.g. Margrave -- Some Facts About The Wick Calculus / N. Lerner -- Schatten Properties For Pseudo-differential Operators On Modulation Spaces / J. Toft. Hans G. Feichtinger ... [et Al.] ; Editors, Luigi Rodino, M.w. Wong. Includes Bibliographical References And Index. Also Issued Online. Front Matter....Pages i-xxiv Banach Gelfand Triples for Gabor Analysis....Pages 1-33 Four Lectures in Semiclassical Analysis for Non Self-Adjoint Problems with Applications to Hydrodynamic Instability....Pages 35-77 An Introduction to Numerical Methods of Pseudodifferential Operators....Pages 79-133 Some Facts About the Wick Calculus....Pages 135-174 Schatten Properties for Pseudo-Differential Operators on Modulation Spaces....Pages 175-202 Back Matter....Pages 203-204 Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-24, 2006