Professeur de l'Enseignement Supérieur
Faculté des Sciences de Rabat
Laboratoire d'Analyse et Applications, 
Unité de Recherche Associée au CNRST (URAC n° 03)
Département de Mathématiques,

Mohammed V University in Rabat
BP 1014, Avenue Ibn Battouta, 10006, Rabat.
e-mails : elfallah@fsr.ac.ma ; omar.elfallah@gmail.com
 




Scientific Interests

Banach Algebras and invariant subspaces

  • Closed ideal theory. 

  • Norm estimates of resolvant, Norm controlled solutions of Bézout identity
  • Reflexivity of operators.


Analytic function spaces

  • Dirichlet spaces.

  • Cyclicity and invariant subspaces.
  • Carleson measures and mutipliers.
  • Kernel estimates and capacity.
  • Zero sets and Interpolation.
  • Composition operators compactness and approximation numbers.
  • Weighted Bergman spaces

  • Toeplitz operators, boundedness, compactness and membership to Schatten classes.
  • Cyclicity in large weighted Bergman spaces.


Some selected publications (Complete list of publications)


Book
  • El-Fallah, Omar; Kellay, Karim; Mashreghi, Javad; Ransford, Thomas. Titre: A primer on the Dirichlet space. Cambridge Tracts in Mathematics, 203. Cambridge University Press, Cambridge, 2014. xiv+211 pp. ISBN: 978-1-107-04752-5
Journals
  • O. El-Fallah, H. Mahzouli, I. Marrhich, H. Naqos, Toeplitz operators on harmonically weighted Bergman spaces and applications to composition operators. J.M.A.A. (2018).
  • O.El-Fallah, Y.Elmadani, K.Kellay, Kernel estimate and capacity in the Dirichlet spaces.  J. Funct. Anal. (2018)
  • O. El-Fallah, Y. Elmadani, K. Kellay, Cyclicity and invariant subspaces in the Dirichlet spaces.  J. Funct. Anal. 270 (9) (2016) 3262-3279.
  • O. El-Fallah, H. Mahzouli, I. Marrich, H. Naqos, Asymtotic behavior of eignevalues of Toeplitz operators on weighted analytic spaces. J. Funct. Anal. 270 (12) (2016) 4614-4630.
  • Borichev, A.; El-Fallah, O.; Hanine, A. Cyclicity in weighted Bergman type spaces. J. Math. Pures Appl. (9) 102 (2014), no. 6, 104--1061.
  • El-Fallah, O.; El Ibbaoui, M.; Naqos, H. Composition operators with univalent symbol in Schatten classes. J. Funct. Anal. 266 (2014), no. 3, 1547--1564.
  • El-Fallah, Omar; Kellay, Karim; Seip, Kristian Cyclicity of singular inner functions from the corona theorem. J. Inst. Math. Jussieu 11 (2012), no. 4, 815--824.
  • El-Fallah, O.; Kellay, K.; Shabankhah, M.; Youssfi, H. Level sets and composition operators on the Dirichlet space. J. Funct. Anal. 260 (2011), no. 6, 1721--1733.
  • Benlarbi Delai, M'hammed; El-Fallah, Omar; Elhachimi, Khalid Réflexivité d'une extension d'un opérateur sous-normal par un opérateur algébrique. J. Funct. Anal. 258 (2010), no. 8, 2586--2600.
  • El-Fallah, Omar; Kellay, Karim; Ransford, Thomas On the Brown-Shields conjecture for cyclicity in the Dirichlet space. Adv. Math. 222 (2009), no. 6, 2196--2214.
  • Bourhim, A.; El-Fallah, O.; Kellay, K. Boundary behaviour of functions of Nevanlinna class. Indiana Univ. Math. J. 53 (2004), no. 2, 347--395.
  • El-Fallah, Omar; Ransford, Thomas Extremal growth of powers of operators satisfying resolvent conditions of Kreiss-Ritt type. J. Funct. Anal. 196 (2002), no. 1, 135--154.
  • El-Fallah, O.; Ezzaaraoui, A. Majorations uniformes de normes d'inverses dans les algèbres de Beurling. J. London Math. Soc. (2) 65 (2002), no. 3, 705--719.
  • El-Fallah, O.; Nikol'skii, N. K.; Zarrabi, M. Estimates for resolvents in Beurling-Sobolev algebras. (Russian) Algebra i Analiz 10 (1998), no. 6, 1--92; translation in St. Petersburg Math. J. 10 (1999), no. 6, 901--964.