We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schrödinger-type differential operator). Using tools such as scattering approach and eigenvalue interlacing inequalities we derive several formulas relating the number of the zeros of the n-th eigenfunction to the spectrum of the graph and of some of its subgraphs. In a special case of the so-called dihedral graph we prove an explicit formula that only uses the lengths of the edges, entirely bypassing the information about the graph’s eigenvalues. The results are explained from the point of view of the dynamics of zeros of the solutions to the scattering problem
Abstract The Euler characteristic i.e., the difference between the number of vertices |V| and edges ...
Differential operators on metric graphs are investigated. It is proven that vertex matching (boundar...
Abstract. We study the first eigenvalue of the p−Laplacian (with 1 < p < ∞) on a quantum graph...
We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs wi...
In this dissertation, we analyze characteristics of eigenfunctions of the Schrödinger operator on g...
Abstract. We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros ...
The Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a w...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
We start by reviewing the notion of "quantum graph", its eigenfunctions and the problem of counting ...
This thesis consists of four papers concerning topics in the spectral theory of quantum graphs, whic...
This thesis consists of four papers and deals with the spectral theory of quantum graphs. A quantum ...
Abstract. Sturm’s oscillation theorem states that the nth eigenfunction of a Sturm-Liouville operato...
In the present theses we study spectral and resonance properties of quantum graphs. First, we consid...
A quantum graph is a weighted combinatorial graph equipped with a Hamiltonian operator acting on fun...
AbstractA notion of splines is introduced on a quantum graph Γ. It is shown that eigen values of a H...
Abstract The Euler characteristic i.e., the difference between the number of vertices |V| and edges ...
Differential operators on metric graphs are investigated. It is proven that vertex matching (boundar...
Abstract. We study the first eigenvalue of the p−Laplacian (with 1 < p < ∞) on a quantum graph...
We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs wi...
In this dissertation, we analyze characteristics of eigenfunctions of the Schrödinger operator on g...
Abstract. We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros ...
The Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a w...
The nodal domains of eigenvectors of the discrete Schrödinger operator on simple, finite and connect...
We start by reviewing the notion of "quantum graph", its eigenfunctions and the problem of counting ...
This thesis consists of four papers concerning topics in the spectral theory of quantum graphs, whic...
This thesis consists of four papers and deals with the spectral theory of quantum graphs. A quantum ...
Abstract. Sturm’s oscillation theorem states that the nth eigenfunction of a Sturm-Liouville operato...
In the present theses we study spectral and resonance properties of quantum graphs. First, we consid...
A quantum graph is a weighted combinatorial graph equipped with a Hamiltonian operator acting on fun...
AbstractA notion of splines is introduced on a quantum graph Γ. It is shown that eigen values of a H...
Abstract The Euler characteristic i.e., the difference between the number of vertices |V| and edges ...
Differential operators on metric graphs are investigated. It is proven that vertex matching (boundar...
Abstract. We study the first eigenvalue of the p−Laplacian (with 1 < p < ∞) on a quantum graph...