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Semiclassical limits of the Schrödinger kernels on the \(h\)-Heisenberg group. (English) Zbl 1317.35272

The author considers the \(h\)-Heisenberg group which is defined by inserting the parameter \(h>0\) in the group law, which approaches the Euclidean case as \(h\) goes to 0. He constructs the Schrödinger kernel of the sub-Laplacian and of the full Laplacian, he characterizes both of them as tempered distributions on \(\mathbb R^{2n+1}\) and shows that their limits as \(h\) goes to \(0\) exist. All the above are called semiclassical limits.

MSC:

35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.
35H20 Subelliptic equations
35K08 Heat kernel
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