An indefinite convection–diffusion operator with real spectrum

An indefinite convection-diffusion operator with real spectrum

has only real eigenvalues, which were shown to exist by Davies in [3]. In the same paper, he showed that the spectrum of −iH is equal to the set of its eigenvalues, so this implies that the spectrum is real. This was conjectured in [1], and Chugunova and Pelinovsky proved in [2] that all but finitely many eigenvalues are real, and gave numerical evidence that all eigenvalues are real. Our appro...

An Indefinite Convection-Diffusion Operator

We give a mathematically rigorous analysis which confirms the surprising results in a recent paper [2] of Benilov, O’Brien and Sazonov about the spectrum of a highly singular non-self-adjoint operator that arises in a problem in fluid mechanics. MSC-class: 34Lxx, 76Rxx, 65F15, 65Q05 keywords: spectrum, non-self-adjoint, fluid mechanics, pseudospectra, eigenvalue, basis.

On the Fučik Spectrum with Indefinite Weights

Hilbert ’ s epsilon as an Operator of Indefinite Committed Choice

Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert’s ε-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the ε-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the ε as a choice operator. After reviewing the literature on semantics of Hilbert’s epsilon operat...

Hilbert's epsilon as an operator of indefinite committed choice

Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert’s ε-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the ε-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the ε as a choice operator. After reviewing the literature on semantics of Hilbert’s epsilon operat...