论文标题
Vladimirov-Taibleson操作员对非交通性Vilenkin组的基本解决方案
Fundamental solution of the Vladimirov-Taibleson operator on noncommutative Vilenkin groups
论文作者
论文摘要
获得了恒定级非交通性vilenkin基团的vladimirov-taibleson操作员的基本溶液和热度分数，以及对相关的热核的一些估计。我们还展示了在$ p $ - 亚洲的海森伯格集团和$ p $ - 亚迪·恩格尔集团上的“弗拉基米罗夫·拉普拉斯人”的基本解决方案，并讨论了我们的结果可能扩展到毕业的$ P $ -Acadic Lie Groups的更普遍的同质运营商。
The fundamental solution and the heat semigroup of the Vladimirov-Taibleson operator on constant-order noncommutative Vilenkin groups are obtained, together with some estimates on the associated heat kernel. We also show the existence of a fundamental solution for the "Vladimirov Laplacian" on the $p$-adic Heisenberg group and the $p$-adic Engel group, and discuss possible extensions of our results to more general homogeneous operators on graded $p$-adic Lie groups.
