Abstract
We extend the results of a previous paper to arbitrary non-integrable but polynomially bounded functions defined over any connected semi-simple Lie group of real-rank one. Our approach is based on the method of bilateral horospheres and is a direct generalisation of that used earlier. All the features of the more restricted transform are retained in this more general formalism.
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Macfadyen, N.W. A Laplace transform on the Lorentz groups. Commun.Math. Phys. 34, 297–314 (1973). https://doi.org/10.1007/BF01646475
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DOI: https://doi.org/10.1007/BF01646475