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On Kac’s principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group
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by Michael Ruzhansky and Durvudkhan Suragan PDF
Proc. Amer. Math. Soc. 144 (2016), 709-721 Request permission

Abstract:

In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac’s “principle of not feeling the boundary”. This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian. We also obtain similar results for higher powers of the Kohn Laplacian.
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Additional Information
  • Michael Ruzhansky
  • Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
  • MR Author ID: 611131
  • Email: m.ruzhansky@imperial.ac.uk
  • Durvudkhan Suragan
  • Affiliation: Institute of Mathematics and Mathematical Modelling, 125 Pushkin Str., 050010 Almaty, Kazakhstan
  • Email: suragan@math.kz
  • Received by editor(s): January 26, 2015
  • Published electronically: June 26, 2015
  • Additional Notes: The authors were supported in part by EPSRC grant EP/K039407/1 and by the Leverhulme grant RPG-2014-02, as well as by MESRK grant 5127/GF4.
  • Communicated by: Joachim Krieger
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 709-721
  • MSC (2010): Primary 35R03, 35S15
  • DOI: https://doi.org/10.1090/proc/12792
  • MathSciNet review: 3430847