Fourier transform of a gaussian measure on the Heisenberg group
Barczy, Mátyás ; Pap, Gyula
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006), p. 607-633 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2006__42_5_607_0,
     author = {Barczy, M\'aty\'as and Pap, Gyula},
     title = {Fourier transform of a gaussian measure on the Heisenberg group},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {42},
     year = {2006},
     pages = {607-633},
     doi = {10.1016/j.anihpb.2005.07.002},
     mrnumber = {2259978},
     zbl = {1102.60003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2006__42_5_607_0}
}

Barczy, Mátyás; Pap, Gyula. Fourier transform of a gaussian measure on the Heisenberg group. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) pp. 607-633. doi : 10.1016/j.anihpb.2005.07.002. http://gdmltest.u-ga.fr/item/AIHPB_2006__42_5_607_0/

[1] R.B. Ash, Real Analysis and Probability, Academic Press, New York, 1972. | MR 435320

[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. | MR 771994 | Zbl 0562.60010

[3] M. Chaleyat-Maurel, Densités des diffusions invariantes sur certains groupes nilpotents. Calcul d'aprés B. Gaveau, Astérisque 84-85 (1981) 203-214. | Zbl 0474.60063

[4] E.B. Davies, Heat Kernels and Spectral Theory, Cambridge University Press, 1989. | MR 990239 | Zbl 0699.35006

[5] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1965. | Zbl 0918.65002

[6] W. Hazod, E. Siebert, Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups, Kluwer Academic Publishers, Drodrecht, 2001. | MR 1860249 | Zbl 1002.60002

[7] H. Heyer, Probability Measures on Locally Compact Groups, Springer, Berlin, 1977. | MR 501241 | Zbl 0376.60002

[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. | MR 1439509 | Zbl 0870.60007

[9] G. Pap, Uniqueness of embedding into a Gaussian semigroup on a nilpotent Lie group, Arch. Math. (Basel) 62 (1994) 282-288. | MR 1259845 | Zbl 0804.60007

[10] G. Pap, Fourier transform of symmetric Gauss measures on the Heisenberg group, Semigroup Forum 64 (2002) 130-158. | MR 1867200 | Zbl 0989.60006

[11] K.R. Parthatsarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967. | MR 226684 | Zbl 0153.19101

[12] B. Roynette, Croissance et mouvements browniens d'un groupe de Lie nilpotent et simplement connexe, Z. Wahr. Verw. Gebiete 32 (1975) 133-138. | MR 394909 | Zbl 0312.60036

[13] E. Siebert, Fourier analysis and limit theorems for convolution semigroups on a locally compact group, Adv. Math. 39 (1981) 111-154. | MR 609202 | Zbl 0469.60014

[14] E. Siebert, Absolute continuity, singularity, and supports of Gauss semigroups on a Lie group, Monatsh. Math. 93 (1982) 239-253. | MR 661571 | Zbl 0477.60008

[15] M.E. Taylor, Noncommutative Harmonic Analysis, Math. Surveys Monogr., vol. 22, American Mathematical Society, Providence, RI, 1986. | MR 852988 | Zbl 0604.43001

[16] W. Tomé, The Representation Independent Propagator for General Lie Groups, World Scientific, Singapore, 1998. | MR 1628602

[17] D. Wehn, Probabilities on Lie groups, Proc. Natl. Acad. Sci. USA 48 (1962) 791-795. | MR 153042 | Zbl 0111.14104