| Eigenvalue Problem and Estimates for a Class of Nilpotent Lie Group |
| Received:January 23, 2000 |
| Key Words:
eigenvalue problem Laplacian nilpotent Lie group.
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| Abstract: |
| In this paper we discuss the spectral properties of the Laplacian on the nilpotentLie group Hn×Rk.We show that the nonexistence of eigenvalue on the whole space by usingthe unitary representation theory and the existence of Dirichlet’s eigenvalue on the boundeddomain of Hn×Rk with the extension of Friedrichs'method to classical Laplacian.We alsogive the estimates of the gap by establishing some useful relation of invariant vector fields. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2003.01.016 |
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