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arXiv · 1211.4144

Sign-indefinite second order differential operators on finite metric graphs

Amru Hussein
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Abstract

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.

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Amru Hussein. 2012-11-17. Sign-indefinite second order differential operators on finite metric graphs. https://doi.org/10.1142/s0129055x14300039

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