Non‐Self‐Adjoint Differential Operators

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Pseudospectra in non-Hermitian quantum mechanics (2014, background): “The importance of this property is summarized by the following statement from [25]: Very large pseudospectra are always associated with eigenvalues which are very unstable with respect to perturbations.”
Form boundedness of the general second‐order differential Operator (2004, background): “inequalities, might be useful in further applications to mathematical physics, dynamics, analysis of phases, and other nonlinear problems (see, e.g., [BB1], [BB2], [ D3 ], [IM]).”
Pseudospectra of semiclassical (pseudo‐) differential operators (2004, background): “The purpose of this paper is to show how some results from the theory of partial differential equations apply to the study of pseudospectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics; see [6] [29].”
Pseudospectrum and Black Hole Quasinormal Mode Instability (2020, methodology): “[2,6,8,9,11]), there seems to be (to our knowledge) no systematic application in the gravitational context.”
Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices (2005, methodology): “First, we observe that by Myers’s theorem (which extends easily to orbifolds; see [5]), the universal orbifold cover X̃ of X is also a compact toric SDE 4-orbifold of positive scalar curvature, so we may assume that X = X̃.”