Browsing by Author "Kostenko, Aleksey"
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- ItemMini-Workshop: Self-adjoint Extensions in New Settings(Zürich : EMS Publ. House, 2019) Kostenko, Aleksey; Pankrashkin, KonstantinThe main focus of the workshop is on the analysis of boundary value problems for differential and difference operators in some non-classical geometric settings, such as fractal graphs, sub-Riemannian manifolds or non-elliptic transmission problems. Taking into account their importance in modern mathematical analysis, we aim at developing suitable tools in the operator theory to deal with the new problem settings.
- ItemSpectral Theory of Infinite Quantum Graphs(Cham (ZG) : Springer International Publishing AG, 2018) Exner, Pavel; Kostenko, Aleksey; Malamud, Mark; Neidhardt, HagenWe investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection together with spectral theory of (unbounded) discrete Laplacians on infinite graphs, we prove a number of new results on spectral properties of quantum graphs. Namely, we prove several self-adjointness results including a Gaffney-type theorem. We investigate the problem of lower semiboundedness, prove several spectral estimates (bounds for the bottom of spectra and essential spectra of quantum graphs, CLR-type estimates) and study spectral types.