37 citations · 81 across the 8 of their papers we have counts for
4 papers · 1 filter
Quasi-isospectrality on quantum graphs
Ralf Rueckriemen
Consider two quantum graphs with the standard Laplace operator and non-Robin type boundary conditions at all vertices. We show that if their eigenvalue-spectra agree everywhere asi…
Quantum graphs and their spectra
Ralf Rueckriemen
We show that families of leafless quantum graphs that are isospectral for the standard Laplacian are finite. We show that the minimum edge length is a spectral invariant. We give a…
Isospectral Metrics on Projective Spaces
Ralf Rueckriemen
We construct isospectral non isometric metrics on real and complex projective space. We recall the construction using isometric torus actions by Carolyn Gordon in chapter 2. In cha…
Recovering quantum graphs from their Bloch spectrum
Ralf Rueckriemen
We define the Bloch spectrum of a quantum graph to be the collection of the spectra of a family of Schrodinger operators parametrized by the cohomology of the quantum graph. We sho…