Some results on non-self-adjoint operators, a survey

2008/04/23 by Johannes Sjoestrand, Sjoestrand, Johannes
Computer Science · Mathematics · #35K65 #35P20 #35Q99 #35S99 #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.AP #math.SP #msc:35K65 #msc:35P20 #msc:35Q99 #msc:35S99

paper · pdf · doi:10.48550/arxiv.0804.3701

arxiv created 2008/04/23 · openalex publication_date 2008/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl asymptotics for the eigenvalues of non-self-adjoint operators with small random perturbations. In the introduction we also review the notion of pseudo-spectrum and its relation to non-self-adjoint spectral problems.

Citations

• Isotropic Hypoellipticity and Trend to Equilibrium for the Fokker-Planck Equation with a High-Degree Potential
• Perturbations of Jordan Matrices

Related

• Spectral properties of non-self-adjoint operators
• Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations
• Pseudospectra and eigenvalue asymptotics for disordered non-selfadjoint operators in the semiclassical limit
• Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators
• Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions IIIa. One branching point