227 citations · 812 across the 43 of their papers we have counts for
31 papers · 1 filter
Trace formulas and inverse spectral theory for generalized indefinite strings
Jonathan Eckhardt, Aleksey Kostenko
Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonica…
Laplacians on infinite graphs: discrete vs continuous
Aleksey Kostenko, Noema Nicolussi
There are two main notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Bo…
A Glazman-Povzner-Wienholtz Theorem on graphs
Aleksey Kostenko, Mark Malamud, Noema Nicolussi
The Glazman-Povzner-Wienholtz theorem states that the completeness of a manifold, when combined with the semiboundedness of the Schrödinger operator and suitable local regu…
Generalized indefinite strings with purely discrete spectrum
Jonathan Eckhardt, Aleksey Kostenko
We establish criteria for the spectrum of a generalized indefinite string to be purely discrete and to satisfy Schatten-von Neumann properties. The results can be applied to the is…
Heat kernels of the discrete Laguerre operators
Aleksey Kostenko
For the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the he…
Self-adjoint and Markovian extensions of infinite quantum graphs
Aleksey Kostenko, Delio Mugnolo, Noema Nicolussi
We investigate the relationship between one of the classical notions of boundaries for infinite graphs, \emph{graph ends}, and self-adjoint extensions of the minimal Kirchhoff Lapl…