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Toka Diagana, Ph.D.
Professor
Address
Department of Mathematics
Howard University
Washington DC 20059
Office
ASB 209
ph: 202-806-7123
fax: 202-806-6831
e-mail: tdiagana@howard.edu
My personal web page
Education
Ph. D. (1999) Université Claude Bernard - Lyon, France
Research Interests: Operator Theory, p-adic Functional Analysis, Abstract Differential Equations, Functional Differential Equations, Integrodifferential Equations, Stochastic Differential Equations, and Difference Equations.
Most interesting phenomena encountered in our daily life can be described through differential equations. In recent years, my goal has been to study the existence of solutions to abstract differential equations in various classes of functions such as almost periodic functions, almost automorphic functions, pseudo almost periodic functions, pseudo almost automorphic functions as well as weighted pseudo almost periodic functions we recently introduced in the literature. One of my current goals consists of studying singular and fractional differential equations in connection with the above-mentioned classes of functions.
It is well-known that the best way to understand properties of linear operators is through their spectral analysis. In particular, the spectral theory for linear operators plays a crucial role in several fields including quantum mechanics. Except for a few investigations such as the pioneer work of Vishik, there is no general spectral theory for linear operators in the non-archimedean setting. One of my current goals consists of developing a general spectral theory for unbounded linear operators on non-archimedean Banach spaces.
Latest Book
Pseudo Almost Periodic Functions in Banach Spaces, Nova Science Publishers, New York, 2007
Selected Publications
- Existence of Weighted Pseudo Almost Periodic Solutions to Some Classes of Hyperbolic Evolution Equations. Journal of Mathematical Analysis and Applications 350 (2009), no. 1, 18-28.
- Almost Periodic Solutions to Some Semilinear Nonautonomous Thermoelastic Plate Equations. Journal of Mathematical Analysis and Applications 349 (2009), no. 1, pp. 74-84 (with M. Baroun; S. Boulite; and L. Maniar)
- Functional Calculus for a Class of Unbounded Linear Operators on Some Non-Archimedean Banach Spaces. Commentationes Mathematicae Univ. Carolin. 50 (2009), no. 1, 37-60 (with Dodzi Attimu)
- Existence of S2-Almost Periodic Solutions to a Class of Nonautonomous Stochastic Evolution Equations. Electronic Journal of Qualitative Theory of Differential Equations, 35 (2008), 1-19 (with P. H. Bezandry)
- Asymptotically Almost Periodic Solutions to Some Classes of Second-Order Functional Differential Equations. Differential and Integral Equations, 21 (2008), no. 5-6, pp. 575-600 (with Henriquez, Hernan R.; and Hernandez M., Eduardo)
- Population models in almost periodic environments. Journal of Difference Equations and Applications, 13 (2007), no. 4, pp. 239-260. (with Elaydi, Saber; Yakubu, Abdul-Aziz)
- Weighted pseudo almost periodic functions and applications. Comptes Rendus Mathématiques de l’Académie des Sciences Paris 343 (2006), no. 10, pp. 643-646.
- Fractional powers of the algebraic sum of normal operators. Proceedings of the American Mathematical Society 134 (2006), no. 6, pp. 1777-1782.
- Towards a Theory of Some Unbounded Linear Operators on p-adic Hilbert Spaces and Applications. Annales Mathématiques Blaise Pascal, 12 (2005), no. 1, pp. 205-222.
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