21 citations · 93 across the 15 of their papers we have counts for
15 papers
Optimal eigenvalues on a metric graph with densities
Kiyan Naderi, Noema Nicolussi
We introduce and study Laplacians on a finite metric graph endowed with generalized densities, that is, measures of finite mass. One important motivation is that this setting provi…
Higher rank inner products, Voronoi tilings and metric degenerations of tori
Omid Amini, Noema Nicolussi
We introduce higher rank inner products on real and complex vector spaces and study their corresponding Voronoi tilings. We use the framework to describe metric degenerations of po…
Capacity of infinite graphs over non-Archimedean ordered fields
Florian Fischer, Matthias Keller, Anna Muranova +1
In this article we study the notion of capacity of a vertex for infinite graphs over non-Archimedean fields. In contrast to graphs over the real field monotone limits do not need t…
A note on Spectral Analysis of Quantum graphs
Noema Nicolussi
We provide an introductory review of some topics in spectral theory of Laplacians on metric graphs. We focus on three different aspects: the trace formula, the self-adjointness pro…
Moduli of hybrid curves II: Tropical and hybrid Laplacians
Omid Amini, Noema Nicolussi
The present paper is a sequel to our work on hybrid geometry of curves and their moduli spaces. We introduce a notion of hybrid Laplacian, formulate a hybrid Poisson equation, and…
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…
Moduli of hybrid curves I: Variations of canonical measures
Omid Amini, Noema Nicolussi
The present paper is the first in a series devoted to the study of asymptotic geometry of Riemann surfaces and their moduli spaces. We introduce the moduli space of hybrid curves a…
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…
Trace formulas and continuous dependence of spectra for the periodic conservative Camassa-Holm flow
Jonathan Eckhardt, Aleksey Kostenko, Noema Nicolussi
This article is concerned with the isospectral problem \[ -f'' + \frac{1}{4} f = zωf + z^2 \upsilon f \] for the periodic conservative Camassa-Holm flow, where is a periodic re…
Quantum graphs on radially symmetric antitrees
Aleksey Kostenko, Noema Nicolussi
We investigate spectral properties of Kirchhoff Laplacians on radially symmetric antitrees. This class of metric graphs enjoys a rich group of symmetries, which enables us to obtai…
Strong Isoperimetric Inequality for Tessellating Quantum Graphs
Noema Nicolussi
We investigate isoperimetric constants of infinite tessellating metric graphs. We introduce a curvature-like quantity, which plays the role of a metric graph analogue of discrete c…
On the Hamiltonian-Krein index for a non-self-adjoint spectral problem
Aleksey Kostenko, Noema Nicolussi
We investigate the instability index of the spectral problem on the line , where is rea…
Spectral Estimates for Infinite Quantum Graphs
Aleksey Kostenko, Noema Nicolussi
We investigate the bottom of the spectra of infinite quantum graphs, i.e., Laplace operators on metric graphs having infinitely many edges and vertices. We introduce a new definiti…