Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations, Fachbücher

- Introduction. - Part I Basic Notions, Differential Operators in One Dimension. - Spectrum and Pseudo-Spectrum. - Weyl Asymptotics and Random Perturbations in a One-Dimensional Semi-classical Case. - Quasi-Modes and Spectral Instability in One Dimension. - Spectral Asymptotics for More General Operators in One Dimension. - Resolvent Estimates Near the Boundary of the Range of the Symbol. - The Complex WKB Method. - Review of Classical Non-self-adjoint Spectral Theory. - Part II Some General Results. - Quasi-Modes in Higher Dimension. - Resolvent Estimates Near the Boundary of the Range of the Symbol. - From Resolvent Estimates to Semigroup Bounds. - Counting Zeros of Holomorphic Functions. - Perturbations of Jordan Blocks. - Part III Spectral Asymptotics for Differential Operators in Higher Dimension. - Weyl Asymptotics for the DampedWave Equation. - Distribution of Eigenvalues for Semi-classical Elliptic Operators with Small Random Perturbations, Results and Outline. - Proof I: Upper Bounds. - Proof II: Lower Bounds. - Distribution of Large Eigenvalues for Elliptic Operators. - Spectral Asymptotics for PT Symmetric Operators. - Numerical Illustrations.