On a semigroup of measures with irregular densities
Colloquium Mathematicae (2000)
- Volume: 83, Issue: 1, page 85-99
- ISSN: 0010-1354
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Abstract
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topGadziński, Przemysław. "On a semigroup of measures with irregular densities." Colloquium Mathematicae 83.1 (2000): 85-99. <http://eudml.org/doc/210776>.
@article{Gadziński2000,
abstract = {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.},
author = {Gadziński, Przemysław},
journal = {Colloquium Mathematicae},
keywords = {Heisenberg group; Fourier transform; semigroup of measures},
language = {eng},
number = {1},
pages = {85-99},
title = {On a semigroup of measures with irregular densities},
url = {http://eudml.org/doc/210776},
volume = {83},
year = {2000},
}
TY - JOUR
AU - Gadziński, Przemysław
TI - On a semigroup of measures with irregular densities
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 1
SP - 85
EP - 99
AB - 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.
LA - eng
KW - Heisenberg group; Fourier transform; semigroup of measures
UR - http://eudml.org/doc/210776
ER -
References
top- [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. Zbl0629.43001
- [2] L. Hörmander, The Analysis of Linear Differential Operators I, Springer, 1983. Zbl0521.35001
- [3] N. M. Matveev, Differential Equations, Leningrad, 1963 (in Russian).
- [4] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Academic Press, 1975. Zbl0308.47002
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