Eigenfunctions of the Laplace–Beltrami Operator on Harmonic \(NA\) Groups
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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 \(\beta >0\).
KeywordsEigenfunctions Poisson transform Harmonic \(NA\) group
Mathematics Subject ClassificationPrimary 43A85 Secondary 22E25
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.