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Local Solvability of Laplacian Difference Operators Arising from the Discrete Heisenberg Group

  • Keri A. Kornelson (a1)
Abstract

Differential operators Dx , Dy , and Dz are formed using the action of the 3-dimensional discrete Heisenberg group G on a set S, and the operators will act on functions on S. The Laplacian operator is a difference operator with variable differences which can be associated to a unitary representation of G on the Hilbert space L 2(S). Using techniques from harmonic analysis and representation theory, we show that the Laplacian operator is locally solvable.

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References
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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