Fundamental solutions for the two dimensional affine group and H<sup>n+1</sup>

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Journal Article
Journal of Mathematical Analysis and Applications, 2017, 445 (1), pp. 953 - 970
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© 2016 Elsevier Inc. We derive the wave and heat kernels on the ax+b group, as well as the fundamental solution of the group Laplacian. We make particular use of the Kontorovich–Lebedev transform and a recent result of the author to produce new expressions for these kernels. Our results easily extend to the hyperbolic space Hn+1 for any n and the explicit formulas are given in n dimensions.
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