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Approximate identities from Laguerre functions and singular integrals on the Heisenberg group

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Abstract

Suitably scaled Laguerre functions are an approximate identity for multiplicative convolution with test functions on the half line. As an application, we derive a precise connection between the Mikhlin-type expansion of a singular integral operator on a Heisenberg groupH n and its natural restriction toH n modulo the center.

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Authors and Affiliations

  1. Department of Mathematics, Yale University, 06520, New Haven, CT, USA

    Richard Beals

  2. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Ontario, Canada

    Peter Greiner

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  1. Richard Beals
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  2. Peter Greiner
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Correspondence to Richard Beals.

Additional information

Research supported by NSF Grant DMS-9800605 and by NSERC Grant OGP0003017.

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Beals, R., Greiner, P. Approximate identities from Laguerre functions and singular integrals on the Heisenberg group. J. Anal. Math. 89, 213–237 (2003). https://doi.org/10.1007/BF02893082

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  • DOI: https://doi.org/10.1007/BF02893082

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