On a semigroup of measures with irregular densities

• Autorzy: Przemysław Gadziński
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 83
• Numer: 1
• Strony: 85-99

Daty

wydano

2000

otrzymano

1998-03-31

poprawiono

1999-08-06

Twórcy

autor

Przemysław Gadziński

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] P. Głowacki and A. Hulanicki, A semi-group of probability measures with non-smooth differential densities on a Lie group, Colloq. Math. 51 (1987), 131-139.
• [2] L. Hörmander, The Analysis of Linear Differential Operators I, Springer, 1983.
• [3] N. M. Matveev, Differential Equations, Leningrad, 1963 (in Russian).
• [4] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Academic Press, 1975.