Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators - Tapa blanda

Sinopsis

Preface.- 1 Basic Notions of Phase Space Analysis.- 1.1 Introduction to pseudodifferential operators.- 1.2 Pseudodifferential operators on an open subset of Rn.- 1.3 Pseudodifferential operators in harmonic .- 2 Metrics on the Phase Space.- 2.1 The structure of the phase space.- 2.2 Admissible metrics.- 2.3 General principles of pseudodifferential calculus.- 2.4 The Wick calculus of pseudodifferential operators.- 2.5 Basic estimates for pseudodifferential operators.- 2.6 Sobolev spaces attached to a pseudodifferential calculus.- 3 Estimates for Non-selfadjoint Operators.- 3.1 Introduction.- 3.2 First bracket analysis.- 3.3 The geometry of condition (Y).- 3.4 The necessity of condition (Y).- 3.5 Estimates with loss of k/k + 1 derivative.- 3.6 Estimates with loss of one derivative.- 3.7 (Y) does not imply solvability with loss of one derivative.- 3.8 (Y) implies solvability with loss of 3/2 derivatives.- 3.9 Open problems.- 4 Appendix.- 4.1 Some elements of Fourier analysis.- 4.2 Some remarks of algebra.- 4.3 Lemmas of classical analysis.- 4.4 On the symplectic and metaplectic groups.- 4.5 Composing a large number of symbols.- 4.6 A few elements of operator theory.- 4.7 On Sjöstrand algebra.- 4.8 On preparation theorems.- 4.9 On the pseudospectrum.- 4.10 More on symbolic calculus.

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