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The Laguerre Calculus on the Heisenberg Group

  • R. W. Beals
  • P. C. Greiner
  • J. Vauthier
Part of the Mathematics and Its Applications book series (MAIA, volume 18)

Abstract

The purpose of this article is to derive a multiplicative symbolic calculus for left-invariant convolution operators on the Heisenberg group. We let Hn denote the n-th Heisenberg group with underlying manifold
$${R^{2n + 1}} = \left\{ {\left( {{x_0},x'} \right)} \right\} = \left\{ {\left( {{x_0},{x_1},...,{x_{2n}}} \right)} \right\},$$
(1.1)
and with the group law
$$xy = \left( {{x_0},x'} \right)\left( {{y_0},y'} \right)$$
$$= \left( {{x_0} + {y_0} + \frac{1}{2}\sum\limits_{j = l}^n {{a_j}\left[ {{x_j}{y_{j + n}} - {x_{j + n}}{y_j}} \right]} ,x' + y'} \right).$$
(1.2)
.

Keywords

HEISENBERG Group Convolution Operator Infinite Matrix Zygmund Operator Twisted Convolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • R. W. Beals
    • 1
    • 2
    • 3
  • P. C. Greiner
    • 1
    • 2
    • 3
  • J. Vauthier
    • 1
    • 2
    • 3
  1. 1.Yale UniversityUSA
  2. 2.The University of TorontoCanada
  3. 3.Universitè de Paris VIFrance

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