Analysis on Extended Heisenberg Group
- [1] CNRS, Toulouse. On leave of absence from Imperial College London.
Annales de la faculté des sciences de Toulouse Mathématiques (2011)
- Volume: 20, Issue: 2, page 379-405
- ISSN: 0240-2963
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topZegarliński, B.. "Analysis on Extended Heisenberg Group." Annales de la faculté des sciences de Toulouse Mathématiques 20.2 (2011): 379-405. <http://eudml.org/doc/219787>.
@article{Zegarliński2011,
abstract = {In this paper we study Markov semigroups generated by Hörmander-Dunkl type operators on Heisenberg group.},
affiliation = {CNRS, Toulouse. On leave of absence from Imperial College London.},
author = {Zegarliński, B.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Heisenberg group; Hörmander-Dunkl operators; Coxeter group; Demazure operator; Markov semigroup; coercive inequalities; ultracontractivity estimates; heat kernel; Gaussian bounds},
language = {eng},
month = {4},
number = {2},
pages = {379-405},
publisher = {Université Paul Sabatier, Toulouse},
title = {Analysis on Extended Heisenberg Group},
url = {http://eudml.org/doc/219787},
volume = {20},
year = {2011},
}
TY - JOUR
AU - Zegarliński, B.
TI - Analysis on Extended Heisenberg Group
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/4//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 2
SP - 379
EP - 405
AB - In this paper we study Markov semigroups generated by Hörmander-Dunkl type operators on Heisenberg group.
LA - eng
KW - Heisenberg group; Hörmander-Dunkl operators; Coxeter group; Demazure operator; Markov semigroup; coercive inequalities; ultracontractivity estimates; heat kernel; Gaussian bounds
UR - http://eudml.org/doc/219787
ER -
References
top- Aronson (D.G.).— Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4) 22 (1968) 607-694, Addendum, 25, p. 221-228 (1971). Zbl0182.13802MR435594
- Alekseevsky (D.), Kriegl (A.), Losik (M.) and Michor (P.W.).— Reflection Groups on Riemannian Manifolds, Annali di Mathematica Pura ed Applicata.
- Bakry (D.), Baudoin (F.), Bonnefont (M.) and Chafaï (D.).— On gradient bounds for the heat kernel on the Heisenberg group, J. Funct. Anal. 255, p. 1905-1938 (2008). Zbl1156.58009MR2462581
- Beals (R.), Gaveau (B.) and Greiner (P.C.).— Hamiltonian-Jacobi Theory and Heat Kernel On Heisenberg Groups, J. Math. Pures Appl. 79, p. 633-689 (2000). Zbl0959.35035MR1776501
- Benjamini (I.), Chavel (I.) and Feldman (A.).— Heat Kernel Lower Bounds on Riemannian Manifolds Using the Old Idea of Nash, Proc. of the London Math. Soc. 1996 s3-72(1):215-240; doi:10.1112/plms/s3-72.1.215 Zbl0853.58098MR1357093
- Bonfiglioli (A.), Lanconelli (E.), and Uguzzoni (F.).— Stratified Lie Groups and Potential Theory for their Sub-Laplacians, Springer Monographs in Mathematics, Springer (2007). Zbl1128.43001MR2363343
- Chow (B.), Lu Peng and Ni Lei.— Hamilton’s Ricci Flow, Grad. Stud. Math., Amer. Math. Soc. (2006). Zbl1118.53001MR2274812
- Davies (E.B.).— Heat kernels and spectral theory. Cambridge University Press, Cambridge, 197 pp (1989). Zbl0699.35006MR990239
- Davies (E.B.).— Explicit Constants for Gaussian Upper Bounds on Heat Kernels, American Journal of Mathematics, Vol. 109, No. 2 (Apr., 1987) p. 319-333, http://www.jstor.org/stable/2374577 Zbl0659.35009MR882426
- Davies (E.B.).— Heat Kernel Bounds for Second Order Elliptic Operators on Riemannian Manifolds, Amer. J. of Math. Vol. 109, No. 3 (Jun., 1987) p. 545-569, http://www.jstor.org/stable/2374567 Zbl0648.58037MR892598
- Davies (E.B.) and Simon (B.).— Ultra-contractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal. 59, p. 335-395 (1984). Zbl0568.47034MR766493
- Driver (B.K.) and Melcher (T.).— Hypoelliptic heat kernel inequalities on the Heisenberg group, J. Funct. Anal. 221, p. 340-365 (2005). Zbl1071.22005MR2124868
- Eldredge (N.).— Precise estimates for the subelliptic heat kernel on H-type groups, J. Math. Pures Appl. 92, p. 52-85 (2009). Zbl1178.35096MR2541147
- Eldredge (N.).— Gradient estimates for the subelliptic heat kernel on H-type groups J. Funct. Anal. (2009), http://dx.doi.org/doi:10.1016/j.jfa.2009.08.012. Zbl1185.43004MR2557945
- Fukushima (M.).— Dirichlet Forms and Markov Processes, North Holland (1980). Zbl0422.31007MR569058
- Gross (L.).— Logarithmic Sobolev inequalities, Amer. J. Math. 97, p. 1061-1083 (1975). Zbl0318.46049MR420249
- Grigor’yan (A.).— Gaussian Upper Bounds for the Heat Kernel on Arbitrary Manifolds, J. Differential Geometry 45, 33-52 (1997). Zbl0865.58042MR1443330
- Guionnet (A.) and Zegarliński (B.).— Lectures on logarithmic Sobolev inequalities. Séminaire de Probabilités, XXXVI, p. 1-134, Lecture Notes in Math., 1801, Springer, Berlin (2003). Zbl1125.60111MR1971582
- Hebisch (W.) and Zegarliński (B.).— Coercive inequalities on metric measure spaces, J. Funct. Anal. 258, p. 814-851 (2010), http://dx.doi.org/doi:10.1016/j.jfa.2009.05.016. Zbl1189.26032MR2558178
- Inglis (J.), Kontis (V.) and Zegarliński (B.).— From -bounds to Isoperimetry with applications to H-type groups, http://arxiv.org/abs/0912.0236. Zbl1210.26017
- Grayson (M.) and Grossman (R.).— Nilpotent Lie algebras and vector fields, Symbolic Computation: Applications to Scientific Computing, R. Grossman, ed., SIAM, Philadelphia, p. 77-96 (1989). MR1022023
- Junqiang Han, Pengcheng Niu and Wenji Qin.— Hardy Inequalities in Half Spaces of the Heinsenberg Group, Bull. Korean Math. Soc. 45, p. 405-417 (2008). Zbl1158.35339MR2442182
- Li (H.-Q.).— Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg, J. Funct. Analysis 236, p. 369-394 (2006). Zbl1106.22009MR2240167
- P. Ługiewicz (P.) and Zegarliński (B.).— Coercive inequalities for Hörmander type generators in infinite dimensions, J. Funct. Anal. 247 p. 438-476 (2007), http://dx.doi.org/doi:10.1016/j.jfa.2007.03.00. Zbl1128.58009
- Masatoshi Noumi.— Painlevé Equations through Symmetry, Translations of Math. Monographs, vol. 223, AMS (2004). Zbl1077.34003MR2044201
- Rösler (M.).— Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators, Communications on Matematical Physics 192, p. 519-541 (1998). Zbl0908.33005MR1620515
- Varopoulos (N.), Saloff-Coste (L.) and Coulhon (T.).— Analysis and Geometry on Groups, Cambridge University Press (1992). Zbl1179.22009MR1218884
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