Inverse problem for the differential pencil on an arbitrary graph with partial information given on the coefficients
type: Item
instance of: scholarly article
title: Inverse problem for the differential pencil on an arbitrary graph with partial information given on the coefficients
zbMATH Open document ID: 1430.34022
published in: Analysis and Mathematical Physics
publication date: 2019-11-28T00:00:00Z
review text: The inverse spectral problem is studied for the differential equations \[ -y_j''(x_j)+(q_j(x_j)+2\lambda p_j(x_j)-\lambda^2)y_j(x_j)=0,\; j=\overline{1,m}, \] on an arbitrary compact geometrical graph with \(m\) edges. The inverse problem consists in recovering the potentials on one edge from a part of the spectrum provided that the potentials are known on the remaining part of the graph. The main results of the paper are the uniqueness theorem and a constructive procedure for the solution of this inverse problem.
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34B45
zbMATH DE Number: 7138549
zbMATH Keywords: differential pencil
zbMATH Keywords: quantum graph
zbMATH Keywords: inverse problem
zbMATH Keywords: uniqueness theorem
zbMATH Keywords: constructive algorithm
author: Natalia Bondarenko
reviewed by: V. A. Yurko
MaRDI profile type: Publication
full work available at URL: s13324-018-0244-6
OpenAlex ID: W2885486944
cites work: Quantum Graphs and Their Applications
cites work: Graph models for waves in thin structures
cites work: Q4664614
cites work: Inverse spectral problems for differential operators on spatial networks
cites work: Q4183612
cites work: Q3695595
cites work: Q3760860
cites work: Q4530224
cites work: Q3937007
cites work: On half inverse problem for differential pencils with the spectral parameter in boundary conditions
cites work: Inverse problems for second-order differential pencils with Dirichlet boundary conditions
cites work: Inverse spectral problems for energy-dependent Sturm–Liouville equations
cites work: Reconstruction of energy-dependent Sturm-Liouville equations from two spectra
cites work: Recovering differential pencils on compact graphs
cites work: An inverse problem for differential pencils on graphs with a cycle
cites work: Inverse problems for differential pencils on A-graphs
cites work: A partial inverse problem for the differential pencil on a star-shaped graph
cites work: An Inverse Sturm–Liouville Problem with Mixed Given Data
cites work: Inverse problem for the Sturm--Liouville equation on a simple graph
cites work: Inverse spectral problems for the Sturm-Liouville operator on a \(d\)-star graph
cites work: Inverse problems for the differential operator on a graph with cycles
cites work: Inverse problems on a graph with loops
cites work: A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph
cites work: Partial inverse problems for Sturm–Liouville operators on trees
cites work: A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph
cites work: Partial inverse problems for the Sturm-Liouville operator on a star-shaped graph with different edge lengths
cites work: Asymptotics of eigenvalues and eigenfunctions of energy-dependent Sturm-Liouville equations
cites work: On recovering the Dirac operator with an integral delay from the spectrum
cites work: INTERPOLATION BY MEANS OF SPECIAL CLASSES OF ENTIRE FUNCTIONS AND RELATED EXPANSIONS IN SERIES OF EXPONENTIALS
Wikidata QID: Q129477498
DOI: 10.1007/S13324-018-0244-6
description: scientific article; zbMATH DE number 7138549