Publications
Theses
February 1998: Doctorat d’état (Habilitation), Mohammed 5 University in Rabat, Morocco.
Dissertation: Algèbres de Beurling. Théorie spectrale et sous espaces hyperinvariants.May 1991: Thèse, University of Bordeaux I, France. Dissertation: Idéaux fermés de L1(R+).
Book
El-Fallah, Omar; Kellay, Karim; Mashreghi, Javad; Ransford, Thomas. Title: 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
El-Fallah, O., Elibbaoui, M. Trace estimates of Toeplitz operators on Bergman spaces and applications to composition operators. Rev. Mat. Iberoam. 38 (2022), no. 6, 1723-1762.
El-Fallah, O. Y. Elmadani, I. Lbghail, Extremal functions and invariant subspaces in Dirichlet spaces. Adv. Math. 408 (2022), 29 pp.
El-Fallah, O., F. Mkadmi, Y. Omari, Integration operators on Hardy and Bergman spaces. Results Math. 77 (2022), no. 5, Paper No. 200, 21 pp.
Bourass, M.;El-Fallah, O.; Marrhich, I.; Naqos, H. On singular values of Hankel operators on Bergman spaces. J. Funct. Anal. 283 (2022), no. 3, 41 pp.
Bahajji-El Idrissi, H.; El-Fallah, O.; Kellay, K. Havin-Mazya type uniqueness theorem for Dirichlet spaces. Bull. Sci. Math. 168 (2021), Paper No. 102967, 14 pp.
Bahajji-El Idrissi, H.; El-Fallah, O.. Blaschke products and zero sets in weighted Dirichlet spaces. Potential Anal. 53 (2020), no. 4, 1299–1316.
Bahajji-El Idrissi, H. ; El-Fallah, O. Approximation in spaces of analytic functions. Studia Math. 255 (2020), no. 2, 209–217.
El-Fallah, O., Elmadani Y., Kellay K., Kernel estimate and capacity in the Dirichlet spaces. Journal of Functional Analysis. Volume 276, Issue 3, 1 February 2019, Pages 867-895
El-Fallah, O., Elmadani Y., Kellay K., Cyclicity and invariant subspaces in the Dirichlet spaces. Journal of Functional Analysis. 270, No. 9, 3262-3279 (2016).
El-Fallah, O., Kellay K., Nevanlinna counting function and pull back measure. Proc. Am. Math. Soc. 144, No. 6, 2559-2564 (2016).
El-Fallah, O., Fricain E., Kellay, K. Mashreghi J., Ransford T., Constructive approximation in de Branges-Rovnyak spaces. Constr. Approx., 44, No. 2, 269-281 (2016).
El-Fallah, O., Mahzouli H., Marrich I., Naqos N., Asymptotic behavior of eignevalues of Toeplitz operators on weighted analytic spaces. J. Funct. Anal. (2016), http://dx.doi.org/10.1016/j.jfa.2016.01.005.
El-Fallah, O., Kellay K., Klaja H., Mashreghi J., Ransford T., Dirichlet spaces with superharmonic weights and de Branges-Rovnyak spaces. Complex Anal. Oper. The- ory 10 (2016), no. 1, 97-107.
Benazzouz, H.; El-Fallah, O.; Kellay, K.; Mahzouli, H. Contact points and Schatten composition operators. Math. Z. 279 (2015), no. 1-2, 407–422.
El-Fallah, O.; Kellay, K.; Mashreghi, J.; Ransford, T. One-box conditions for Carleson measures for the Dirichlet space. Proc. Amer. Math. Soc. 143 (2015), no. 2, 679–684.
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, O.; Kellay, K.; Seip, K. 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.
El-Fallah, O.; Kellay, K.; Ransford, T. Cantor sets and cyclicity in weighted Dirichlet spaces. J. Math. Anal. Appl. 372 (2010), no. 2, 565–573.
Bouya, B.; El-Fallah, O.; Kellay, K. Idéaux fermés d’algèbres de Beurling analytiques sur le bidisque. Bull. Sci. Math. 134 (2010), no. 6, 588–604.
Benlarbi Delai, M.; El-Fallah, O.; Elhachimi, K. Réflexivité d’une extension d’un opérateur sous-normal par un opérateur algébrique. J. Funct. Anal. 258 (2010), no. 8, 2586–2600.
El-Fallah, O.; Kellay, K.; Ransford, T. On the Brown-Shields conjecture for cyclicity in the Dirichlet space. Adv. Math. 222 (2009), no. 6, 2196–2214.
El-Fallah, O.; Kellay, K. ; Ransford, T. Cyclicity in the Dirichlet space. Ark. Mat. 44 (2006), no. 1, 61–86.
El-Fallah, O.; Zarrabi, M. Estimations des solutions de l’équation de Bézout dans les algèbres de Beurling analytiques. Math. Scand. 96 (2005), no. 2, 307–319.
Benlarbi Delai, M;El-Fallah, O. Réflexivité d’une extension d’un opérateur normal par un opérateur nilpotent. J. Funct. Anal. 223 (2005), no. 1, 28–43.
El-Fallah, O.; Ransford, T. Peripheral point spectrum and growth of powers of operators. J. Operator Theory 52 (2004), no. 1, 89–101.
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, O.; Ransford, T. 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.
Bourhim, A.; El-Fallah, O.; Kellay, Karim Comportement radial des fonctions de la classe de Nevanlinna. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), no. 6, 529–532.
Daoui, A.; El-Fallah, O. Localisation spectrale et sous-espaces hyperinvariants. (French) [Spectral localization and hyperinvariant subspaces] Proc. Amer. Math. Soc. 127 (1999), no. 7, 2117–2122.
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.
El-Fallah, O.; Kellay, K. Sous-espaces biinvariants pour certains shifts pondérés. Ann. Inst. Fourier (Grenoble) 48 (1998), no. 5, 1543–1558.
El-Fallah, O. Idéaux fermés de L1(R+). Math. Scand. 72 (1993), no. 1, 120–130.
Publications in proceedings
Bourass, M.; El-Fallah, O.; Marrhich, I.; Naqos, H.; Toeplitz and Hankel operators on Bergman spaces. Extended abstracts fall 2019—spaces of analytic functions: approximation, interpolation, sampling, 51–57, Trends Math. Res. Perspect. CRM Barc., 12.
E.Abakoumov, O. El-Fallah, K.Kellay, T.Ransford, Cyclicity in the harmonic Dirich- let space. Harmonic Analysis, Function Theory, Operator Theory and Their Applications. Theta Foundation International Book Series of Mathematical Texts 22, 1-11 (2018).
El-Fallah, Omar; Kellay, Karim; Mashreghi, Javad; Ransford, Thomas A self-contained proof of the strong-type capacitary inequality for the Dirichlet space. Complex analysis and potential theory, 1-20, CRM Proc. Lecture Notes, 55, Amer. Math. Soc., Providence, RI, 2012.
El-Fallah, Omar; Kellay, Karim; Ransford, Thomas Invariant subspaces of the Dirich- let space. Hilbert spaces of analytic functions, 133-141, CRM Proc. Lecture Notes, 51, Amer. Math. Soc., Providence, RI, 2010.