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| 摘要: |
| 本文研究了具有加权测度dμ=e-φdv的H型群G上漂移Laplace算子-△G+<▽Gφ，▽G（·）>的Dirichlet特征值问题，建立了该问题的Levitin-Parnovski型特征值不等式，推广包含了Ilias和Makhoul对Heisenberg群上次Laplace算子所获得的结果（J.Geom.Anal.，2012，22（1）：206-222）. |
| 关键词: H型群 特征值 漂移Laplace算子 |
| DOI： |
| 分类号:O175.9;O186.1 |
| 基金项目:国家自然科学基金资助（11001130）；中央高校基本科研业务费专项基金资助（30917011335）. |
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| LEVITIN-PARNOVSKI-TYPE INEQUALITY FOR EIGENVALUES OF THE DRIFTING LAPLACIAN ON THE H-TYPE GROUP WITH THE WEIGHTED MEASURE |
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HAN Cheng-yue,SUN He-jun,JIANG Xu-yong
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| Abstract: |
| In this paper, we study the Dirichlet eigenvalue problem of the drifting Laplacian -△G + <▽Gφ, ▽G (·)> on the H-type group G with the weighted measured dμ=e-φdv. We establish a Levitin-Parnovski universal inequality for eigenvalues of this problem, which generalize the result derived by Ilias and Makhoul for the Kohn Laplacian on the Heisenberg group (J. Geom. Anal., 2012, 22(1):206-222). |
| Key words: H-type group eigenvalue drifting Laplacian |
