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# 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.

### 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},
}