Related papers: Cospectral quantum graphs
Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation…
We study self-adjoint extensions of a second order differential operator of Sturm-Liouville type on a graph. We relate self-adjointness of the operator to the existence of non-complete trajectories of the Hamiltonian vector field defined by…
We consider the spectral structure of indefinite second order boundary-value problems on graphs. A variational formulation for such boundary-value problems on graphs is given and we obtain both full and half-range completeness results. This…
We introduce a new biharmonic Steklov problem on differential forms with Dirichlet-type boundary conditions and show that it is elliptic. We prove the existence of a discrete spectrum for this problem and give variational characterizations…
Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and…
We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex conditions on a finite metric graph and a corresponding Titchmarsh-Weyl function (a parameter-dependent Neumann-to-Dirichlet map). We give a complete…
We comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint boundary…
We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The…
We obtain a complete asymptotic expansion for the eigenvalues of the Dirichlet-to-Neumann maps associated with Schr\"odinger operators on compact Riemannian surfaces with boundary. For the zero potential, we recover the well-known spectral…
Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating properties of the eigenfunctions are studied. The spectral…
We study cospectral vertices on finite graphs in relation to the echolocation problem on Riemannian manifolds. First, We prove a computationally simple criterion to determine whether two vertices are cospectral. Then, we use this criterion…
This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and…
We consider the spectral problems for the Sturm-Liouville operator generated by the Dirichlet, Neumann, Dirichlet-Neumann and Neumann-Dirichlet conditions. The necessary and sufficient condition for the coincidence of the spectrum of the…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…
In this paper, inequalities among eigenvalues of different self-adjoint discrete Sturm-Liouville problems are established. For a fixed discrete Sturm-Liouville equation, inequalities among eigenvalues for different boundary conditions are…
Consider two inverse problems for Sturm-Liouville problems on the unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is…
This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…