25 citations · 38 across the 7 of their papers we have counts for
7 papers
Recovering the shape of a quantum tree by two spectra
Vyacheslav Pivovarchik
We show how to find the shape of an equilateral tree using the spectra of the Neumann and the Dirichlet problems generated by the Sturm-Liouville equation. In case of snowflake tre…
Distinguishing co-spectral quantum graphs by scattering
Delio Mugnolo, Vyacheslav Pivovarchik
We propose a simple method for resolution of co-spectrality of Schrödinger operators on metric graphs. Our approach consists of attaching a lead to them and comparing the -funct…
On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem
Olga Boyko, Olga Martynyuk, Vyacheslav Pivovarchik
Spectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with the Dirichlet boundary conditions at the pendant vertices and continuity and Ki…
Cospectral quantum graphs
Anastasia Chernyshenko, Vyacheslav Pivovarchik
Spectral problems are considered generated by the Sturm-Liouville equation on connected simple equilateral graphs with the Neumann and Dirichlet boundary conditions at the pendant…
Characteristic functions under series and parallel connection of quantum graphs
Vyacheslav Pivovarchik
For a graph consisting of parallel connected subgraphs we express the characteristic function of the boundary value problem with generalized Neumann conditions at both joining poin…
On string density at the origin
Israel Kac, Vyacheslav Pivovarchik
In [V. Barcilon Explicit solution of the inverse problem for a vibrating string. J. Math. Anal. Appl. {\bf 93} (1983) 222-234] two boundary value problems were considered generated…
Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings
Vyacheslav Pivovarchik, Natalia Rozhenko, Christiane Tretter
We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root…