Toka Diagana, Ph.D.
Department of Mathematics
Washington DC 20059
Room 240 Annex III
My personal web page Click Here
Ph. D. (1999) Université Claude Bernard - Lyon 1, 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.
Almost Periodic Stochastic Processes,
Springer, New York, 2011 (with P.H. Bezandry)
Pseudo Almost Periodic Functions in Banach Spaces,
Nova Science Publishers, New York, 2007
information on my other publications, see my personal
- Existence of Pseudo
Almost Automorphic Mid Solutions to Some Nonautonomous Second-Order
Differential Equations. Rocky
Mountain Journal of Mathematics (in press), February, 2011.
- Almost Periodic Solutions to
Second-Order Nonautonomous Differential Equations. Proceedings of
the American Mathematical Society (in press), December, 2010
- Almost Automorphic Mild
Some Classes of Hyperbolic Evolution Equations. Journal of
Mathematical Analysis and Applications 350 (2009),
no. 1, pp. 18-28
- Existence of Weighted Pseudo
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
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)
- Asymptotically Almost
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
- Population models in almost
environments. Journal of Difference Equations and Applications, 13
(2007), no. 4, pp. 239-260. (with Elaydi, Saber; Yakubu, Abdul-Aziz)
- Weighted pseudo almost
functions and applications. Comptes Rendus Mathématiques de
l’Académie des Sciences Paris 343 (2006), no. 10,
- Fractional powers of the
sum of normal operators. Proceedings of the American Mathematical
Society 134 (2006), no. 6, pp. 1777-1782.
- The African Acadamy of Sciences
- Emerging Scholar Award (Howard
University, April, 2006)
- "Prix Chinguitt" (December, 2006)
- Ibni Oumar Mahamat Saleh Prize Panel
- The American Mathematical Society
"Committee on Human Rights of Mathematicians"
- The American Mathematical Society "Books
and Journal Donations Steering Committee"