Trace formulae for Schrödinger operators on metric graphs with applications to recovering matching conditions

Abstract

The paper is a continuation of the study started in [8]. Schrödinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of $\delta$ type. Either an infinite series of trace formulae (provided that edge potentials are infinitely smooth) or a finite number of such formulae (in the cases of $L_1$ and $C^M$ edge potentials) are obtained which link together two different quantum graphs under the assumption that their spectra coincide. Applications are given to the problem of recovering matching conditions for a quantum graph based on its spectrum.

Key words: Quantum graphs, Schrödinger operator, Sturm-Liouville problem, inverse spectral problem, trace formulae, boundary triples.

Full Text

Article Information

Title	Trace formulae for Schrödinger operators on metric graphs with applications to recovering matching conditions
Source	Methods Funct. Anal. Topology, Vol. 20 (2014), no. 2, 134-148
MathSciNet	MR3242862
zbMATH	1313.34093
Milestones	Received 22/10/2013; Revised 20/03/2014
Copyright	The Author(s) 2014 (CC BY-SA)

Authors Information

Yulia Ershova
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Alexander V. Kiselev
Department of Higher Mathematics and Mathematical Physics, St. Petersburg State University, 1 Ulianovskaya, St. Petersburg, St. Peterhoff, 198504, Russia 

Citation Example

Yulia Ershova and Alexander V. Kiselev, Trace formulae for Schrödinger operators on metric graphs with applications to recovering matching conditions, Methods Funct. Anal. Topology 20 (2014), no. 2, 134-148.

BibTex

@article {MFAT734,
    AUTHOR = {Ershova, Yulia and Kiselev, Alexander V.},
     TITLE = {Trace formulae for Schrödinger operators on metric graphs with applications to recovering matching conditions},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {20},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {134-148},
      ISSN = {1029-3531},
  MRNUMBER = {MR3242862},
 ZBLNUMBER = {1313.34093},
       URL = {http://mfat.imath.kiev.ua/article/?id=734},
}