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Inverse Spectral Problem for Quantum Graphs with Rationally Dependent Edges

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Operator Theory, Analysis and Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 174))

Abstract

In this paper we study the problem of unique reconstruction of the quantum graphs. The idea is based on the trace formula which establishes the relation between the spectrum of Laplace operator and the set of periodic orbits, the number of edges and the total length of the graph. We analyse conditions under which is it possible to reconstruct simple graphs containing edges with rationally dependent lengths.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Lund Institute of Technology, Box 118, 210 00, Lund, Sweden

    Marlena Nowaczyk

Authors
  1. Marlena Nowaczyk
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Editor information

Editors and Affiliations

  1. Institut of Mathematics, Polish Academy of Sciences, ul. Sw. Tomasza 30/7, 31-027, Krakow, Poland

    Jan Janas

  2. Department of Mathematics, Lund Institute of Technology, 221 00, Lund, Sweden

    Pavel Kurasov

  3. Dept. of Mathematics, Imperial College London, Room 675 South Kensington Campus, SW7 2AZ, London, UK

    Ari Laptev

  4. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Ari Laptev

  5. Department of Mathematical Physics, St. Petersburg State University, Ulyanovskaya 1, 198904, St. Petersburg, Russia

    Sergei Naboko

  6. Department of Mathematics, University of Alabama, 452 Campbell Hall, Birmingham, AL, 35294-1170, USA

    GĂĽnter Stolz

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Nowaczyk, M. (2007). Inverse Spectral Problem for Quantum Graphs with Rationally Dependent Edges. In: Janas, J., Kurasov, P., Laptev, A., Naboko, S., Stolz, G. (eds) Operator Theory, Analysis and Mathematical Physics. Operator Theory: Advances and Applications, vol 174. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8135-6_8

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