Invariant differential operators

Oscillations with Several Degrees-of-Freedom

Published in L.M.B.C. Campos, Simultaneous Systems of Differential Equations and Multi-Dimensional Vibrations, 2019

The contravariant metric tensor (8.371b) and the determinant of the covariant metric tensor (8.371c) can be used to write any invariant differential operator (note III.9.43), for example, the scalar Laplacian (III.9.469a) ≡ (8.373a): ∇2≡1h∂∂xigijh∂∂xj=1h∂∂xihhi2∂∂xi,

The heat kernel of sub-Laplace operator on nilpotent Lie groups of step two

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Journal Information

Published in Applicable Analysis, 2021

Der-Chen Chang, Qianqian Kang, Wei Wang

The most important left-invariant differential operator on nilpotent Lie groups of step two is the sub-Laplace operator: where , , and The heat kernel of sub-Laplace operator on is in the sense of distribution.

Invariant differential operators

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Oscillations with Several Degrees-of-Freedom

The heat kernel of sub-Laplace operator on nilpotent Lie groups of step two