71 citations · 183 across the 15 of their papers we have counts for
4 papers · 1 filter
The Birman-Schwinger principle in von Neumann algebras of finite type
Vadim Kostrykin, Konstantin A. Makarov, Anna Skripka
We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As…
On Krein's Example
Vadim Kostrykin, Konstantin A. Makarov
In his 1953 paper [Matem.~Sbornik \textbf{33} (1953), 597 -- 626] Mark Krein presented an example of a symmetric rank one perturbation of a self-adjoint operator such that for all…
The inverse scattering problem for metric graphs and the traveling salesman problem
Vadim Kostrykin, Robert Schrader
We present a solution to the inverse scattering problem for differential Laplace operators on metric noncompact graphs. We prove that for almost all boundary conditions (i) the sca…
Laplacians on Metric Graphs: Eigenvalues, Resolvents and Semigroups
Vadim Kostrykin, Robert Schrader
The main objective of the present work is to study the negative spectrum of (differential) Laplace operators on metric graphs as well as their resolvents and associated heat semigr…