Inverse problems for quantum trees II:Recovering matching conditions for star graphs

Sergei Avdonin; Pavel Kurasov; Marlena Nowaczyk

doi:10.3934/ipi.2010.4.579

Article Contents

2010, Volume 4, Issue 4: 579-598. Doi: 10.3934/ipi.2010.4.579

This issue Previous Article Mathematical reminiscences Next Article The quadratic contribution to the backscattering transform in the rotation invariant case

Inverse problems for quantum trees II: Recovering matching conditions for star graphs

1.
Department of Mathematics and Statistics, University of Alaska, Fairbanks, AK 99775-6660
2.
Dept. of Mathematics, LTH, Lund Univ., Box 118, 221 00 Lund
3.
Institute of Mathematics, PAN, ul. Św.Tomasza 30, 31-027 Kraków

Received: October 31, 2009

Revised: April 30, 2010

Published: October 2010

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Abstract

The inverse problem for the Schrödinger operator on a star graph is investigated. It is proven that such Schrödinger operator, i.e. the graph, the real potential on it and the matching conditions at the central vertex, can be reconstructed from the Titchmarsh-Weyl matrix function associated with the graph boundary. The reconstruction is also unique if the spectral data include not the whole Titchmarsh-Weyl function but its principal block (the matrix reduced by one dimension). The same result holds true if instead of the Titchmarsh-Weyl function the dynamical response operator or just its principal block is known.

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Mathematics Subject Classification: Primary: 81C05, 35R30, 35L05, 93B05, 49E15.

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References

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