227 citations · 812 across the 43 of their papers we have counts for
44 papers
Infinite-peakon solutions of the Camassa-Holm equation
Xiang-Ke Chang, Jonathan Eckhardt, Aleksey Kostenko
We study a class of (conservative) low regularity solutions to the Camassa-Holm equation on the line by exploiting the classical moment problem (in the framework of generalized ind…
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…
The conservative Camassa-Holm flow with step-like irregular initial data
Jonathan Eckhardt, Aleksey Kostenko
We extend the inverse spectral transform for the conservative Camassa-Holm flow on the line to a class of initial data that requires strong decay at one endpoint but only mild boun…
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 note on the Gaffney Laplacian on infinite metric graphs
Aleksey Kostenko, Noema Nicolussi
We show that the deficiency indices of the minimal Gaffney Laplacian on an infinite locally finite metric graph are equal to the number of finite volume graph ends. Moreover, we pr…
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…