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The Journal of Geometric Analysis

, Volume 26, Issue 3, pp 1913–1924 | Cite as

Eigenfunctions of the Laplace–Beltrami Operator on Harmonic \(NA\) Groups

  • Ewa Damek
  • Pratyoosh Kumar
Article

Abstract

We characterize some \(L^p\)-type eigenfunctions of the Laplace–Beltrami operator on harmonic \(NA\) groups corresponding to the eigenvalue \((\rho ^2-\beta ^2)\) for all \(\beta >0\).

Keywords

Eigenfunctions Poisson transform Harmonic \(NA\) group 

Mathematics Subject Classification

Primary 43A85 Secondary 22E25 

Notes

Acknowledgments

This work was completed while both authors were visiting IISc Bangalore India. They are grateful to Prof. S. Thangavelu for his invitation as well as to the staff of the Department of Mathematics there for their kind support and warm hospitality. The authors would like to thank the referee for the valuable comments and suggestions made.

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Copyright information

© Mathematica Josephina, Inc. 2015

Authors and Affiliations

  1. 1.Institute of MathematicsWrocław UniversityWrocławPoland
  2. 2.Department of MathematicsIndian Institute of Technology, GuwahatiGuwahatiIndia

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