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# Trace formulae for graph Laplacians with applications to recovering matching conditions

### Abstract

Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either $\delta$ or $\delta'$ type. In either case, an infinite series of trace formulae which link together two different graph Laplacians provided that their spectra coincide is derived. Applications are given to the problem of reconstructing matching conditions for a graph Laplacian based on its spectrum.

### Article Information

 Title Trace formulae for graph Laplacians with applications to recovering matching conditions Source Methods Funct. Anal. Topology, Vol. 18 (2012), no. 4, 343-359 MathSciNet MR3058461 zbMATH 1289.34088 Copyright The Author(s) 2012 (CC BY-SA)

### Authors Information

Yulia Ershova
Institute of Mathematics, National Academy of Science 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 graph Laplacians with applications to recovering matching conditions, Methods Funct. Anal. Topology 18 (2012), no. 4, 343-359.

### BibTex

@article {MFAT661,
AUTHOR = {Ershova, Yulia and Kiselev, Alexander V.},
TITLE = {Trace formulae for graph Laplacians with applications to recovering matching conditions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {18},
YEAR = {2012},
NUMBER = {4},
PAGES = {343-359},
ISSN = {1029-3531},
MRNUMBER = {MR3058461},
ZBLNUMBER = {1289.34088},
URL = {http://mfat.imath.kiev.ua/article/?id=661},
}