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Sign-indefinite second order differential operators on finite metric graphs

Amru Hussein

subject

Pure mathematicsSpectral theoryScatteringOrder (ring theory)FOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Type (model theory)Mathematics::Spectral TheoryDifferential operator34B45 (Primary) 47B25 34L05 35P20 35P25 81U15 (Secondary)Mathematics - Spectral TheoryMetric (mathematics)FOS: MathematicsScattering theorySpectral Theory (math.SP)Mathematical PhysicsMathematicsSign (mathematics)

description

The question of self-adjoint realizations of sign-indefinite second order differential operators is discussed in terms of a model problem. Operators of the type $-\frac{d}{dx} \sgn (x) \frac{d}{dx}$ are generalized to finite, not necessarily compact, metric graphs. All self-adjoint realizations are parametrized using methods from extension theory. The spectral and scattering theory of the self-adjoint realizations are studied in detail.

yearjournalcountryeditionlanguage
2012-11-17
https://dx.doi.org/10.48550/arxiv.1211.4144