3 papers
math.SP2025
Spectral flow and Robin domains on metric graphs
Ram Band, Marina Prokhorova, Gilad Sofer
This paper is devoted to the Neumann-Kirchhoff Laplacian on a finite metric graph. We prove an index theorem relating the nodal deficiency of an eigenfunction with (1) the Morse in…
math.FA2025
The unitary group in the strong topology and a construction of Dixmier-Douady
Nikolai V. Ivanov, Marina Prokhorova
By a theorem of Dixmier-Douady the unitary group of an infinite-dimensional separable Hilbert space in the strong operator topology is contractible. The Dixmier-Douady proof is…
math.DG2024
Family index for Fredholm extensions of semi-Fredholm operators
Marina Prokhorova
This paper is devoted to Fredholm realizations of semi-Fredholm operators in a Hilbert space. Such a realization is determined by an abstract boundary condition, which is a subspac…