Integral Equations and Operator Theory

, Volume 71, Issue 2, pp 199–223 | Cite as

Resolvent Expansions on Hybrid Manifolds

  • Konstantin Pankrashkin
  • Svetlana Roganova
  • Nader Yeganefar
Article
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Abstract

We study Laplace-type operators on hybrid manifolds, i.e., on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace–Beltrami operators on each component with some boundary conditions at the points of gluing. The large spectral parameter expansion of the trace of the second power of the resolvent is obtained. Some questions of the inverse spectral theory are addressed.

Mathematics Subject Classification (2010)

Primary 35C20 Secondary 47A10 45C05 

Keywords

Asymptotic expansion Laplacian manifold boundary conditions resolvent 
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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Konstantin Pankrashkin
    • 1
  • Svetlana Roganova
    • 2
    • 3
  • Nader Yeganefar
    • 4
  1. 1.Laboratoire de mathématiques d’Orsay, CNRS UMR 8628Université Paris Sud 11Orsay CedexFrance
  2. 2.Institut für MathematikHumboldt-UniversitätBerlinGermany
  3. 3.URSSAFMarseilleFrance
  4. 4.Laboratoire d’Analyse, topologie, probabilités, CNRS UMR 6632Centre de Mathématiques et InformatiqueMarseille CedexFrance

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