5 citations · 9 across the 7 of their papers we have counts for
8 papers
Zero measure Cantor spectrum for aperiodic metric tiling graphs
Ram Band, Gilad Sofer
We study a family of aperiodic metric graphs generated by one-dimensional tilings. We prove that, generically, the spectrum of the associated Kirchhoff Laplacian has Lebesgue measu…
Spectral properties of aperiodic metric and discrete graphs
Gilad Sofer
In this thesis, we study the spectral properties of dynamically defined aperiodic metric and discrete graphs. Our goal is to determine to what extent spectral properties of discret…
Johnson-Schwartzman Gap Labelling for Metric and Discrete Decorated Graphs
Ram Band, Gilad Sofer
We study Schrödinger operators on metric and discrete decorated graphs. The values taken by the integrated density of states (IDS) on spectral gaps are called gap labels. A natural…
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…
Spectral curves of quantum graphs with type vertex conditions
Gilad Sofer
In this Thesis, we study the behavior of spectral curves of quantum graphs under certain families of vertex conditions, called the family, which we define in this work. We fo…
Differences between Robin and Neumann eigenvalues on metric graphs
Ram Band, Holger Schanz, Gilad Sofer
We consider the Laplacian on a metric graph, equipped with Robin (-type) vertex condition at some of the graph vertices and Neumann-Kirchhoff condition at all others. The corres…
Time evolution and the Schrödinger equation on time dependent quantum graphs
Uzy Smilansky, Gilad Sofer
The purpose of the present paper is to discuss the time dependent Schrödinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so…
Three Classification Results In The Theory Of Weighted Hardy Spaces On The Ball
Danny Ofek, Gilad Sofer
We present a natural family of Hilbert function spaces on the d-dimensional complex unit ball and classify which of them satisfy that subsets of the ball yield isometrically isomor…