Sign-indefinite second order differential operators on finite metric graphs

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.

43 pages, 2 figures

References in corpus (2)

• The effective Hamiltonian in curved quantum waveguides under mild regularity assumptions
• Schroedinger equations with indefinite effective mass

Cited by in corpus (3)

• Non-self-adjoint graphs
• Self-adjoint indefinite Laplacians
• Spectral analysis of metamaterials in curved manifolds