$$L^2$$-Poisson integral representations of eigensections of invariant differential operators on a homogeneous line bundle over the complex Grassmann manifold $$SU(r,r+b)/S( U(r)\times U(r+b))$$

Autor: Abdelhamid Boussejra, Noureddine Imesmad, Achraf Ouald Chaib

Publikováno v: Annals of Global Analysis and Geometry. 61:399-426

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b33ead7b1d5844212db4d1f1a8c5b05e
https://doi.org/10.1007/s10455-021-09819-9

L-Poisson integral representations for solutions of the generalized Hua system on line bundles over SU(n,n)/S(U(n)×U(n))

Autor: Abdelhamid Boussejra, Nadia Ourchane

Publikováno v: Journal of Functional Analysis. 280:108824

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::768edf26f83836d37465de63d3d84edb
https://doi.org/10.1016/j.jfa.2020.108824

Lifted infinitesimal holomorphic representation for the n -dimensional complex hyperbolic ball and for Cartan domains of type I

Autor: Abdelhamid Boussejra, Hélène Airault

Publikováno v: Bulletin des Sciences Mathématiques. 137:923-967

The Laplacian and Ornstein–Uhlenbeck operators on the finite dimensional complex ball are obtained from the infinitesimal holomorphic representation of the group U ( n , 1 ) . We compare the invariant measures for these operators with the unitarizi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a43ba43c3ddf3a51f937a0949eb6cf16
https://doi.org/10.1016/j.bulsci.2013.06.004

Lp-Poisson integral representations of solutions of the Hua system on Hermitian symmetric spaces of tube type

Autor: Abdelhamid Boussejra

Publikováno v: Journal of Functional Analysis. 235:413-429

In this paper, we give a necessary and sufficient condition on eigenfunctions of the Hua operator on a Hermitian symmetric space of tube type X = G / K , to have an L p -Poisson integral representations over the Shilov boundary of X . More precisely,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::6e6c43d4f77fd131f27836f3fa3d0162
https://doi.org/10.1016/j.jfa.2005.11.005

Characterization of Poisson integrals on non-tube bounded symmetric domains

Autor: Abdelhamid Boussejra, Koufany Khalid

Publikováno v: Journal de Mathématiques Pures et Appliquées
Journal de Mathématiques Pures et Appliquées, 2007, 87, pp.438-451
Journal de Mathématiques Pures et Appliquées, Elsevier, 2007, 87, pp.438-451
HAL

We characterize the $L^p$-range, $1 < p < +\infty$, of the Poisson transform on the Shilov boundary for non-tube bounded symmetric domains. We prove that this range is a Hua-Hardy type space for harmonic functions satisfying a Hua system.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bbb456ac5553deb5fcaefa0d46c9c3c0
https://hal.science/hal-00095481/file/LpPoissonIntegrals.pdf