In this paper we study Markov semigroups generated by Hörmander-Dunkl type operators on Heisenberg group.
Dans ce travail, nous étudions les semi-groupes de Markov produits par les opérateurs de type d’Hörmander-Dunkl sur le groupe d’Heisenberg.
@article{AFST_2011_6_20_2_379_0,
author = {B. Zegarli\'nski},
title = {Analysis on {Extended} {Heisenberg} {Group}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {379--405},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 20},
number = {2},
year = {2011},
doi = {10.5802/afst.1296},
mrnumber = {2847888},
zbl = {1253.47028},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1296/}
}
TY - JOUR AU - B. Zegarliński TI - Analysis on Extended Heisenberg Group JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2011 SP - 379 EP - 405 VL - 20 IS - 2 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1296/ DO - 10.5802/afst.1296 LA - en ID - AFST_2011_6_20_2_379_0 ER -
%0 Journal Article %A B. Zegarliński %T Analysis on Extended Heisenberg Group %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2011 %P 379-405 %V 20 %N 2 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1296/ %R 10.5802/afst.1296 %G en %F AFST_2011_6_20_2_379_0
B. Zegarliński. Analysis on Extended Heisenberg Group. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 2, pp. 379-405. doi : 10.5802/afst.1296. https://afst.centre-mersenne.org/articles/10.5802/afst.1296/
[1] 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). | Numdam | MR | Zbl
[2] Alekseevsky (D.), Kriegl (A.), Losik (M.) and Michor (P.W.).— Reflection Groups on Riemannian Manifolds, Annali di Mathematica Pura ed Applicata.
[3] 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). | MR | Zbl
[4] 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). | MR | Zbl
[5] 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 | MR | Zbl
[6] Bonfiglioli (A.), Lanconelli (E.), and Uguzzoni (F.).— Stratified Lie Groups and Potential Theory for their Sub-Laplacians, Springer Monographs in Mathematics, Springer (2007). | MR | Zbl
[7] Chow (B.), Lu Peng and Ni Lei.— Hamilton’s Ricci Flow, Grad. Stud. Math., Amer. Math. Soc. (2006). | MR | Zbl
[8] Davies (E.B.).— Heat kernels and spectral theory. Cambridge University Press, Cambridge, 197 pp (1989). | MR | Zbl
[9] 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 | MR | Zbl
[10] 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 | MR | Zbl
[11] 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). | MR | Zbl
[12] Driver (B.K.) and Melcher (T.).— Hypoelliptic heat kernel inequalities on the Heisenberg group, J. Funct. Anal. 221, p. 340-365 (2005). | MR | Zbl
[13] Eldredge (N.).— Precise estimates for the subelliptic heat kernel on H-type groups, J. Math. Pures Appl. 92, p. 52-85 (2009). | MR | Zbl
[14] Eldredge (N.).— Gradient estimates for the subelliptic heat kernel on H-type groups J. Funct. Anal. (2009), . | DOI | MR | Zbl
[15] Fukushima (M.).— Dirichlet Forms and Markov Processes, North Holland (1980). | MR | Zbl
[16] Gross (L.).— Logarithmic Sobolev inequalities, Amer. J. Math. 97, p. 1061-1083 (1975). | MR | Zbl
[17] Grigor’yan (A.).— Gaussian Upper Bounds for the Heat Kernel on Arbitrary Manifolds, J. Differential Geometry 45, 33-52 (1997). | MR | Zbl
[18] 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). | Numdam | MR | Zbl
[19] Hebisch (W.) and Zegarliński (B.).— Coercive inequalities on metric measure spaces, J. Funct. Anal. 258, p. 814-851 (2010), . | DOI | MR | Zbl
[20] Inglis (J.), Kontis (V.) and Zegarliński (B.).— From -bounds to Isoperimetry with applications to H-type groups, . | arXiv
[21] 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). | MR
[22] 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). | MR | Zbl
[23] 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). | MR | Zbl
[24] P. Ługiewicz (P.) and Zegarliński (B.).— Coercive inequalities for Hörmander type generators in infinite dimensions, J. Funct. Anal. 247 p. 438-476 (2007), . | DOI | Zbl
[25] Masatoshi Noumi.— Painlevé Equations through Symmetry, Translations of Math. Monographs, vol. 223, AMS (2004). | MR | Zbl
[26] Rösler (M.).— Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators, Communications on Matematical Physics 192, p. 519-541 (1998). | MR | Zbl
[27] Varopoulos (N.), Saloff-Coste (L.) and Coulhon (T.).— Analysis and Geometry on Groups, Cambridge University Press (1992). | MR | Zbl
Cited by Sources: