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On a semigroup of measures with irregular densities

Przemysław Gadziński — 2000

Colloquium Mathematicae

We study the densities of the semigroup generated by the operator $- X^{2} + | Y |$ on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are $C^{\infty}$ . We give explicit spectral decomposition of images of $- X^{2} + | Y |$ in representations.

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