This article is cited in 28 papers

Brief communications

Ambarzumian's Theorem for a Sturm–Liouville Boundary Value Problem on a Star-Shaped Graph

V. N. Pyvovarchyk

Odessa State Academy of Building and Architecture

Abstract: Ambarzumian's theorem describes the exceptional case in which the spectrum of a single Sturm–Liouville problem on a finite interval uniquely determines the potential. In this paper, an analog of Ambarzumian's theorem is proved for the case of a Sturm–Liouville problem on a compact star-shaped graph. This case is also exceptional and corresponds to the Neumann boundary conditions at the pendant vertices and zero potentials on the edges.

Keywords: inverse problem, Neumann boundary conditions, normal eigenvalue, multiplicity of an eigenvalue, least eigenvalue, minimax principle.

UDC: 517.5+517.43

Received: 24.07.2003

DOI: 10.4213/faa44

 English version: Functional Analysis and Its Applications, 2005, 39:2, 148–151

Bibliographic databases:

• 
• 
• 
• 
•