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Dr. Hocine Guediri

أستاذ مشارك

Faculty

كلية العلوم
Office: 2 A 175 B 4

0114676517
hguediri
السيرة الذاتية

Dr. Hocine Guediri

مختصر السيرة الذاتية
I am a faculty at the Department of Mathematics, College of Science, King Saud University. I have got my PhD in Mathematics from Provence University, France (2001). I am specialized in Functional Analysis and Complex Analysis. My research interests include: Operator on Function Spaces (Toeplitz and Hankel Operator on Hardy and Bergman spaces, Berezin Quantization).
نص السيرة الذاتية

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Contact Information:

Address: 

Dr. Hocine Guediri

Department of Mathematics, College of Science, King Saud University, 

P.O. Box 2455, Riyadh 11451,  Saudi Arabia

Tel: + 966 1 14 67 65 17

Fax: + 966 1 14 67 65 12

E-mail:  hguediri@ksu.edu.sa    and    guediri.hocine@gmail.com 

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Education:

  • Languages:  Arabic,   English   and   French,  as well as German (limited knowledge).
  • Ph.D. (Doctorat):    Provence University , Marseille, France,  2001.
  • M.Sc. (Magistere):    Annaba University, Algeria,  1996.
  • D.E.A.:  Annaba University, Algeria, 1994.
  • B.Sc. (D.E.S.): Mathematics, Constantine University, Algeria,  1993.

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 Professional Activities:

March 2013- ->: Associate Professor, King Saud University, Riyadh (Saudi Arabia).

2001- -March 2013: Assistant Professor, King Saud University, Riyadh (Saudi Arabia).

2000- -2001: Assistantship Position (ATER), Provence University, Marseille (France).

1999- -2000: Research Fellowship, Stuttgart University, Stuttgart (Germany).

1994- -1998: Assistantship Positions, Annaba University, Annaba (Algeria).

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Teaching Experience:

  • Graduate courses:
  1. Real Analysis.
  2. Complex Analysis.
  3. Functional Analysis.
  4. Theory.
  5. Operator Theory, Banach Algebras and C*-algebras.
  6. Operator Theory on Function Spaces.
  7. Geometric Function Theory.
  8. Harmonic Analysis.
  9. Integral Equations.

 

  • Undergraduate courses:
  1. Complex Analysis.
  2. Multivariable Calculus.
  3. Calculus.
  4. Real Analysis.
  5. Linear Algebra.
  6. Vector Calculus.
  7. Algebra.
  8. Ordinary Differential Equations.
  9. Partial differential equations.
  10. Discrete Mathematics.
  11. Topology.
  12. Probability and Statistics

 

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Specialization:   Functional Analysis and Complex Analysis



Research Area:   Operator Theory on Function Spaces



Research Interests:

My recent research interests turns round operator theory on function spaces in the unit disk. The concrete classes of operators I am interested in are Toeplitz, Hankel and dual Toeplitz operators on Hardy and Bergman spaces and their orthogonal complements. More precisely, my interests include their algebraic properties such as intertwining relations, products, commutativity, normality, quasinormality and corresponding Brown-Halmos type theorems, as well as their boundedness and compactness, and also their spectral properties (spectrum, invertibility, numerical range). I am also interested in studying the C*-algebras generated by Toeplitz operators. The Berezin transform is one of the main tools in the investigation of such properties in case of the Bergman space. Owing more properties of this pioneering tool leads to satisfactory information about Toeplitz operators. Hence, this operator attracts my attention as well, along with related aspects in physics namely the Berezin quantization. Currently, I am studying algebraic and spectral properties of Toeplitz operators on the Bergman space of the complex upper half-plane.



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 Publications:

  • [G1] Guediri, H. (with Garayev, M.T. M. Gürdal & G. M. Alsahli): On some problems for operators on the reproducing kernel Hilbert space. Linear and Multilinear Algebra, 2020.
  • [G2] Guediri, H. (with N. Altwaijry, M.T. Garayev and A. Baazeem): Skew-symmetric and essentially unitary operators via the Berezin symbols. Open Mathematics 2020, 18: 1--11.
  • [G3] Guediri, H. (with Garayev, M.T. and Sadraoui, H.): New characterizations of Bloch spaces, Bers-type and Zygmund-type spaces and related Questions. Ufa Mathematical Journal, Vol. 10 (3), pp. 131-141, 2018.
  • [G4] Guediri, H. (with Garayev, M.T. and Sadraoui, H.): Applications of reproducing kernels and Berezin symbols. New York J. Math. 22, 583--604, 2016.
  • [G5] Guediri, H. (with Garayev, M.T. and Sadraoui, H.): On Some Problems in the Space Cn([0, 1]) and related questions. Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 78, no.1, 147--156, 2016.
  • [G6] Guediri, H. (with Garayev, M.T. and Sadraoui, H.): The Bergman space as a Banach Algebra. New York Journal of Mathematics, Vol. 21, pp. 339- - 350, (2015).
  • [G7] Guediri, H. (with Benaissa, L.): Properties of Dual Toeplitz Operators with Applications to Haplitz Products on the Hardy space of the Polydisk. Taiwanese Journal of Mathematics, Vol. 19 no. 1, p.p. 31- - 49, (2015).
  • [G8] Guediri, H. : Products of Toeplitz and Hankel Operators on the Hardy Space of the Unit Sphere. Oper. Theory Adv. Appl., Vol. 236, PP. 243--256 Birkhauser, Springer, Basel, 2014.
  • [G9]Guediri, H. : Dual Toeplitz Operators on the Sphere. Acta Math. Sin. (Engl. Ser.) 29 no. 9, 1791--1808, (2013).
  • [G10] Guediri, H. : Quasinormality and numerical ranges of certain classes of dual Toeplitz operators. Abstract and Applied Analysis, Volume 2010 (2010), Article ID 426319, 14 pages, doi:10.1155/2010/426319.
  • [G11] Guediri, H. : Function theoretic proofs of Brown-Halmos theorems, Arab J. Math. Sc., 13 (2007), 15-26.
  • [G12] Durand, M. and Guediri, H. : Scattering of acoustic waves by a layered elastic obstacle: a direct integral equations approach, Adv. Math. Sci. Appl. 13 (2), (2003), 519-547.
  • [G13] Guediri, H. : On a boundary variational inequality of the second kind modelling friction, Math. Methods Appl. Scie., 25 (2), (2002), 93-114.
  • [G14] Guediri, H. : Characterization of the coincidence set for mixed Signorini problems, Applicable analysis, 77 (3-4), (2001), 327-341.
  • [G15] Guediri, H. : A regularization procedure for a boundary variational inequality of the second kind, Nonlinear Oscillations, 4 (1), (2001), 50-70.
  • [G16] Guediri, H. : A regularization method for a boundary variational inequality of the second kind associated to a friction problem, C. R. Acad. Sci. Paris, Serie IIb Mechanics, 318 (12), (2000), 899-904.
  • [G17] Guediri, H. : Compactness of certain classes of Toeplitz operators on the harmonic Bergman space. Proceedings of the Fourth International Conference on Mathematical Science (ICM2008), United Arab Emirates University, Al-Ain UAE, Vol. 3 PP 911--932, March 03-06, 2008.
  • [G18] Guediri, H. : Qualitative properties and characterization of the solution of a fourth order Signorini contact problem, Proceedings of the six'th meeting of the SAMS, April 9--10 (2002), PP. 17-26.
  • [G19] Durand, M. and Guediri, H. : A new system of integral equations for the elasto-acoustic coupling problem, Mathematical and numerical aspects of wave propagation (Santiago de compostela, 2000), SIAM, Philadelphia, PA, (2000), PP. 143-147.

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Conferences:

  • Invited speaker: First International Workshop on Interaction between Operator Theory and Linear Dynamical Systems, El Jadida, Morocco, June, 27th-29th, 2019.
  • 28th International Workshop on Operator Theory and its Applications (IWOTA 2017), Chemnitz Technical University, Chemnitz, Germany, August 14 - - 18, 2017.
  • Fifth International Conference and School Geometry, Dynamics, Integrable Systems-GDIS 2014: Bicentennial of great Poncelet Theorem and Billiard Dynamics. ICTP, Triest (Italy), June 16 - - 27, 2014.
  • 24th International Workshop on Operator Theory and its Applications (IWOTA 2013), Indian Institute of Science, Bangalore (India), December 16 - - 20, 2013.
  • Advanced School and Workshop on Matrix Geometries and Applications, ICTP, Triest (Italy), July 1 - - 12, 2013.
  • Second Annual Math Days of King Saud University, Riyadh, March 14 - -16, 2012.
  • 22nd International Workshop on Operator Theory and its Applications (IWOTA 2011), University of Sevilla (Spain), July 3- -9, 2011.
  • Conference: Mathematics and its Applications, Al-Imam University, Riyadh, March 23- - 16, 2011.
  • Advanced school and workshop on discrete groups in complex geometry, ICTP, Triest (Italy), June 28 - - July 13, 2010.
  • First Annual Math Days of King Saud University, King Saud University, Riyadh (Saudi Arabia), December 16--17, 2009.
  • The XIXth International Workshop on Operator Theory and its Applications (IWOTA2008), The college of William and Mary, Williamsburg, Virginia, USA, July 22 - July 26, 2008.
  • The Ninth Workshop on Numerical Ranges and Numerical Radii (WONRA), The college of William and Mary, Williamsburg, Virginia, USA, July 19 - July 21, 2008.
  • Symposium on Global Analysis and Probability, Qassim University, Saudi Arabia, May 27--28, 2008.
  • The Fourth International Conference on Mathematical Science (ICM2008), United Arab Emirates University, Al-Ain UAE, March 03-06, 2008.
  • (A joint work with Prof. M.A. Al-Gwaiz) The seven'th meeting of the SAMS on Information Technology in Mathematics, Prince Sultan University, Riyadh (Saudi Arabia), April 7--8, 2004.
  • The six'th meeting of the SAMS, King Saud University, Riyadh (Saudi Arabia), April 9--10, 2002.
  • The fifth International conference on wave propagation, Mathematical and numerical aspects of wave propagation (Santiago de compostela, Spain 2000), SIAM-INRIA-Univ. Santiago de compostela (Spain), July 10-14, 2000.
  • Deuxieme colloque national en analyse fonctionnelle et applications, Sidi Bel Abbes (Algeria), November 17-19, 1997.

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Thesis Supervision:



Ph.D.:

  • Ph.D. thesis supervision in progress, King Saud University, Riyadh, 2021.

  M.Sc.:

  • Berezin Transform and Toeplitz Operators on the Hilbertian Hardy Space.  King Saud University, Riyadh, May 2015.
  • The Riemann Zeta Function and the Prime Number Theorem. King Saud University, Riyadh, May 2014.
  • Fredholm Toeplitz Operators on the Hardy Space over the Circle. King Saud University, Riyadh, May 2012.
  • Quasinormal Toeplitz Operators on the Hilbertian Hardy Space and Halmos' Problem V. King Saud University-- and -- Hail University, Hail, May 2012.
  • Toeplitz Operators on Generalized Hardy Spaces. King Saud University-- and -- Hail University, Hail, May 2012.
  • Spectral properties of Toeplitz operators on the Bergman space. King Saud University, Riyadh, September 2010.
  • Compactness criteria for Toeplitz operators on the Bergman space. King Saud University, Riyadh, July 2009.
  • Algebraic properties of Toeplitz operators on the harmonic Bergman space. King Saud University, Riyadh, December 2008.
  • Products of Bergman space Toeplitz operators and Brown-Halmos type theorems. King Saud University, Riyadh, June 2006.
  • Dual Toeplitz operators versus Toeplitz operators. King Saud University, Riyadh, February 2006.

 

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