Monatshefte für Mathematik

, Volume 123, Issue 1, pp 21–42 | Cite as

Paley-Wiener type theorems on harmonic extensions ofH-type groups

  • Bianca Di Blasio
Article

Abstract

Letn=vz be anH-type group, and letna be the harmonic semidirect product ofn withaR. LetNA be the corresponding simply connected Lie group. If dimv=m and dimz=k, denoteQ=m/2+k. We prove that the spherical Fourier transform is a topological isomorphism between thep-Schwartz spacelp(N,A),(0<p≤2), (0<p≦2), and the space of holomorphic rapidly decreasing functions on the strip {s∈C:|Re(s)|<εQ/2} with ε=2/p−1.

1991 Mathematics Subject Classification

43A30 43A90 53C25 

Key words

harmonic manifold spherical Fourier transform Heisenberg type groups solvable Lie groups 

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Bianca Di Blasio
    • 1
  1. 1.Dipartimento de MatematicaPolitecnico de TorinoTorinoItaly

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