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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## On a semigroup of measures with irregular densities

### Tom 83 / 2000

Colloquium Mathematicum 83 (2000), 85-99 DOI: 10.4064/cm-83-1-85-99

#### Streszczenie

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 $C^∞$. We give explicit spectral decomposition of images of $-X^2+|Y|$ in representations.