Fourier transform of a gaussian measure on the Heisenberg group

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1. [1] R.B. Ash, Real Analysis and Probability, Academic Press, New York, 1972. MR435320
2. [2] P. Baldi, Unicité du plongement d'une mesure de probabilité dans un semi-groupe de convolution gaussien, Cas non-abélien, Math. Z.188 (1985) 411-417. Zbl0562.60010MR771994
3. [3] M. Chaleyat-Maurel, Densités des diffusions invariantes sur certains groupes nilpotents. Calcul d'aprés B. Gaveau, Astérisque84–85 (1981) 203-214. Zbl0474.60063
4. [4] E.B. Davies, Heat Kernels and Spectral Theory, Cambridge University Press, 1989. Zbl0699.35006MR990239
5. [5] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1965. Zbl0918.65002
6. [6] W. Hazod, E. Siebert, Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups, Kluwer Academic Publishers, Drodrecht, 2001. Zbl1002.60002MR1860249
7. [7] H. Heyer, Probability Measures on Locally Compact Groups, Springer, Berlin, 1977. Zbl0376.60002MR501241
8. [8] D. Neuenschwander, Probabilities on the Heisenberg group: Limit theorems and Brownian motion, in: Lecture Notes in Math., vol. 1630, Springer, Berlin, 1996, pp. 379-397. Zbl0870.60007MR1439509
9. [9] G. Pap, Uniqueness of embedding into a Gaussian semigroup on a nilpotent Lie group, Arch. Math. (Basel)62 (1994) 282-288. Zbl0804.60007MR1259845
10. [10] G. Pap, Fourier transform of symmetric Gauss measures on the Heisenberg group, Semigroup Forum64 (2002) 130-158. Zbl0989.60006MR1867200
11. [11] K.R. Parthatsarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967. Zbl0153.19101MR226684
12. [12] B. Roynette, Croissance et mouvements browniens d'un groupe de Lie nilpotent et simplement connexe, Z. Wahr. Verw. Gebiete32 (1975) 133-138. Zbl0312.60036MR394909
13. [13] E. Siebert, Fourier analysis and limit theorems for convolution semigroups on a locally compact group, Adv. Math.39 (1981) 111-154. Zbl0469.60014MR609202
14. [14] E. Siebert, Absolute continuity, singularity, and supports of Gauss semigroups on a Lie group, Monatsh. Math.93 (1982) 239-253. Zbl0477.60008MR661571
15. [15] M.E. Taylor, Noncommutative Harmonic Analysis, Math. Surveys Monogr., vol. 22, American Mathematical Society, Providence, RI, 1986. Zbl0604.43001MR852988
16. [16] W. Tomé, The Representation Independent Propagator for General Lie Groups, World Scientific, Singapore, 1998. Zbl0916.58009MR1628602
17. [17] D. Wehn, Probabilities on Lie groups, Proc. Natl. Acad. Sci. USA48 (1962) 791-795. Zbl0111.14104MR153042