| Sampling Theory | Wavelets | Medical Imaging |
| Fractional Fourier Transform | Sinc Approximations | Boundary-Value Problems |
| Special Functions | Integral Transforms | Generalized Functions |
Below are samples of my publications in these areas, but for a full list of publications, click here.
Sampling Theory (Shannon)
“A q-analogue of the Whittaker-Shannon-Kotel’nikov Sampling
theorem, Proceedings of the American Mathematical Society, Vol. 131, pp. 3711-3719
(2003), (jointly with M. Ismail).
“ Lagrange Interpolation and Sampling Theorems,” jointly with P. Butzer, Chapter 3 in “Theory and Applications of Non-Uniform Sampling,” F. Marvasti, Editor, Kluwer/Plenum Publishing Corporation (2001), pp. 123-168.
“ Sampling on a string," (jointly with A. Boumenir), The Journal
of Fourier Analysis and
Applications, Vol. 8 (2002), pp. 211-231.
“ Advances in Shannon's Sampling Theory," CRC Press, Boca Raton, Florida, 1993.
“ Kramer's sampling theorem for multidimensional signals and its relationship with Lagrange-type interpolation," The Journal of multidimensional systems and signal processing, Vol. 3 (1992), pp. 323-340.
“Construction of orthonormal wavelets using Kampe de Feriet functions," Proceedings of the American Mathematical Society, Vol. 130 (2002), pp.2893-2904.
Wavelets in Closed Forms,” jointly with G. Walter, Chapter 5 in “Wavelet Transforms and Time-frequency Signal Analysis,” L. Debnath, Editor, Birkhäuser Publishing Company (2001) ), pp. 121-143.
“Shannon-type Wavelets and the Convergence of their Associated Wavelet Series,” in “Modern Sampling Theory: Mathematics and Applications,” J. Benedetto and P. Ferreira, Editors, Birkhause Publishing Company (2001), pp. 135-152..
"Pointwise convergence of a class of non-orthogonal wavelet expansions,"
Proceedings of the American Mathematical Society, Vol. 128 (2000),
pp. 3629-3637.
“Texture Identification of Tissues Using Directional Wavelet, Ridgelet, and Curvelet Transforms, in “Frames and Operator Theory in Analysis and Signal Processing,” Contemporary Mathematics Series, American Mathematical Society, Vol. 451, pp. 89-118 (2008).
The Wavelet, Directional Wavelet, and Ridgelet Transforms With Applications
in Texture Identification,” jointly with L. Dettori,, in “Modern
Mathematical Models, Methods and Algorithms for Real World Systems” edited
by A.H. Siddiqi, I. Duff and O.Christensen, Anamaya Publisher, New Delhi-London
(2007).
Fractional Fourier Transform:
“ Fractional Wigner distribution and ambiguity functions,” (jointly with V. B. Shakhmurov) Journal of Fractional Calculus and Applied Analysis, Vol. 6. No. 4 (2003), pp. 473-490
“A class of fractional integral transforms: A generalization of the fractional Fourier transform,” IEEE Transactions on Signal Processing, Vol. 50 (2002), pp. 619-627.
“New Sampling Formulae for the Fractional Fourier Transform,” (jointly with A. Garcia) the Journal of Signal Processing, Vol. 77 (1999), pp. 111-114.
“Hilbert transform associated with the fractional Fourier transform,” IEEE Signal Proc. Letters, Vol 5, No 8 (1998), pp. 206-208.
"A convolution and product theorem for the fractional Fourier transform," IEEE Signal Processing Letters, Vol. 5, No. 4 (1998), pp. 101-103.
"Fractional Fourier transform of generalized functions," Journal of Integral Transforms and Special Functions, Vol. 7 No. 4(1998), pp. 299-312.
"On the relationship between the Fourier and fractional Fourier transforms," IEEE Signal Processing Letters, Vol. 3 (1996), pp. 310-311.
" On the relationship between the fractional Fourier transform and the
Riemann-Liouville fractional
integral, Proceedings of the International Association for Mathematics and
Computers in Simulation
(IMACS), May 2000.
“A comparison between the Adomian decomposition and the sinc-Galerkin
methods for solving
nonlinear boundary-value problems,” (jointly with E. Deeba and J. Yoon)
to appear in the Journal of
Computational Analysis and Applications.
“Sinc-Galerkin method for solving linear sixth order boundary-value problems,” to appear in “Mathematics of Computation,” American Mathematical Society, (jointly with M. El-Gamel and J. Cannon).
“Sinc-Galerkin method for solving non-linear boundary-value problems,” to appear in the International Journal of Computers and Mathematics with Applications, (jointly with M. El-Gamel).
“A Comparison between the wavelet-Galerkin and the Sinc-Galerkin methods in solving non-homogeneous heat equations,” (Jointly with M. El Gamel), Contemporary Mathematics, American Mathematical Society, Vol. 313 (2002), pp. 97-116.
“Discontinuous boundary-value problems: Expansion and sampling theorems,” (jointly with M. Annaby, G. Freiling), Journal of Integral Equations and Applications, Vol. 16 (2004), pp. 1-24.
“An inversion theorem for integral transforms related to singular Sturm-Liouville problems on a half Line,” (jointly with C. Shin), Acta Mathematica Hungaria, Vol. 97 (2002), pp. 273-286.
“Polynomial growth solutions of Sturm-Liouvill equations on a half-line and their zero distribution,” Mathematische Nachrichten, (jointly with C. Shin and A. Tovbis), Vol. 263-264, pp. 204-217, January, 2004 .
"A new role of Green's function in interpolation and sampling theory, "the Journal of Mathematical Analysis and Applications, Vol. 175 (1993), pp. 222-238.
“A q-analogue of the Whittaker-Shannon-Kotel’nikov Sampling theorem, Proceedings of the American Mathematical Society, Vol. 131, pp. 3711-3719 (2003), (jointly with M. Ismail).
"A proof of new summation formulae by using sampling theorems," Proceedings
of the American Mathematical Society, Vol. 117, No. 3 (1993), pp. 699-710.
"A new role of sampling theory in the theory of special functions,"
Proceedings of the 13th IMACS World congress on Computation and Applied
Mathematics, Dublin, Ireland 1991, C. Brezinski, editor, Elsevier Publ.,
Amsterdam (1993).
"Generalized Jacobi transforms," jointly with E. Deeba, the Journal of Applicable Analysis, Vol. 48 (1993), pp. 63-79.
"Jacobi polynomials as generalized Faber polynomials," Transactions of the American Mathematical Society, Vol. 321, No. 1 (1990), pp. 363-378.
"Radon transform of Boehmians," (jointly with P. Mikusinski), Proceedings of the American Mathematical Society, Vol. 118 (1993), pp. 561-570.
"On the inversion of integral transforms associated with Sturm-Liouville problems," jointly with G. Walter, Journal of Mathematical Analysis and Applications, Vol. 164, No. 1(1992), pp. 285-306.
"Inversion of integral transforms associated with a class of perturbed heat equations," jointly with D. Haimo, Journal of Mathematical Analysis and Applications, Vol. 163, No. 1(1992), pp. 113-135.
"Fractional Fourier transform of generalized functions," Journal of Integral Transforms and Special Functions, Vol. 7 No. 4(1998), pp. 299-312.
"Wavelet expansions of analytic hyperfunctions," Journal of Integral Transforms and Special Functions, Vol. 3 (1995), pp. 305-320.
" Wavelet transforms of periodic generalized functions, "the Journal of Mathematical Analysis and Applications., Vol. 183, 2(1994), pp. 391-412.
"Generalized Faber expansions of hyperfunctions on analytic curves," the Journal of the Mathematical Society of Japan, Vol. 42, No. 1 (1990), pp. 155-170.