Ahmed I. Zayed

Education

Editorial Boards
  • Managing Editor, Journal of Sampling Theory in Image and Signal Processing
  • Assistant Editor, The International Journal of Mathematics and Computer Science
  • Associate Editor,Journal of Multidimensional Systems and Signal Processing
  • Associate Editor, Journal of Computational Analysis and Applications
  • Assistant Editor, The International Journal of Mathematics and Mathematical Sciences
  • Associate Editor, International Journal of Fractional Calculus and Applied Analysis
  • Associate Editor, Journal of Generalized Functions
  • Member of the Editorial Board of Journal of Mathematics and Statistics
  • Member of the Editorial Board of the International Journal of Applied Mathematics

Selected publications

Books and chapters
  • Frames and Operator Theory in Analysis and Signal Processing, American Mathematical Society, Contemporary Mathematics Series, Vol 451, 2008.
  • Topics in Harmonic Analysis and Ergodic Theory, American Mathematical Society, Contemporary Mathematics Series, Vol 444, 2007.
  • Sampling, Wavelets, and Tomography, Co-Editor with J. Benedetto, Birkhauser, Boston, 2003.
  • Function and Generalized Function Transformations, CRC Press, Boca Raton, Florida, 1996.
  • Mathematical Analysis, Wavelets and Signal Processing, American Mathematical Society, Contemporary Mathematics Series, Vol. 190 (1995), Co-Editor with M. Ismail, and Z. Nahsed.
  • Advances in Shannon's Sampling Theory, CRC Press, Boca Raton, Florida, 1993.
  • “The Wavelet, Directional Wavelet, and Ridgelet Transforms With Applications in Texture Identification”, (with L. Dettori), in Modern Mathematical Models, Methods and Algorithms for Real World Systems, Anamaya Publisher, New Delhi-London (2007).
  • “Comparison of a Wavelet-Galerkin Procedure With a Crank-Nicolson-Galerkin Procedure for the Diffusion Equation Subject to the Specification of Mass,” Chapter 5, in Mathematical Models and Methods for Real-World systems, Taylor & Francis Group, FL (2005).
  • Chapter on "Wavelets," Encyclopedia of Optical Engineering, CRC Press.
  • "The Zak transform," Encyclopedia of Mathematics, Supplement III, Kluwer Publications
  • “Shannon-type Wavelets and the Convergence of their Associated Wavelet Series,” in Modern Sampling Theory: Mathematics and Applications, Birkhause Publishing Company (2001), pp. 135–152.
  • "Integral Transforms," 30th Edition of CRC Standard Tables and Formulae, CRC Press, FL, 1995.

Articles
  • "A Generalization of the prolate spheroidal wave functions,” Proceedings of the American Mathematical Society, Vol. 135, (2007), pp. 2193–2203
  • “Sampling expansions of functions having values in a Banach space,” Proceedings of the American Mathematical Society, Vol. 133, # 12 (2005), pp. 3597– 3607 (jointly with D. Han).
  • A. Boumenir and A. Zayed, “The equivalence of Kramer and Shannon sampling theorems revisited,” Journal of Sampling Theory in Image and Signal Processing, Vol. 4, No. 3 (2005), pp. 251–269.
  • A comparison between the Adomian decomposition and the sinc-Galerkin methods for solving nonlinear boundary-value problems,” Journal of Computational Analysis and Applications,Vol. 7, No. 1(2005)), pp. 5-20 (jointly with E. Deeba and J. Yoon)
  • “Sinc-Galerkin method for solving non-linear boundary-value problems,” Journal of Computers and Mathematics with Applications, Vol. 48, No. 9 (2004), pp. 1285–1298 (jointly with M. El-Gamel).
  • “Sinc-Galerkin method for solving linear sixth order boundary-value problems,“ Mathematics of Computation,” American Mathematical Society, Vol. 73, No. 247 (2004), pp. 1325-1343 (jointly with M. El-Gamel and J. Cannon).
  • “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).
  • “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 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.
  • "Sampling on a string," (jointly with A. Boumenir), The Journal of Fourier Analysis and Applications, Vol. 8 (2002), pp. 211–231.
  • “Paley-Wiener-type theorem for a class of integral transforms,” (jointly with V. k. Tuan), the Journal of Math. Anal. & Appls, Vol. 266 (2002), pp. 200–226.
  • “Density deconvolution of different conditional distributions,” (jointly with M. Pensky), Annals of the Institute of Statistical Mathematics, Vol. 54 (2002), pp. 701–712.
  • "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.
  • “Generalization of a theorem of Boas to a class of integral transforms,” (jointly with V. k. Tuan), the Journal of Resultät der Mathematik. Vol. 38 (2000), pp. 362–376.
  • "Kramer's sampling theorem with discontinuous kernels," (jointly with A, Garcia), Resultät der Mathematik, Vol. 34 (1998), pp. 197–206.
  • "Multiresolution analysis with sampling subspaces," (jointly with G. Walter), Journal of Fractional Calculus and Applied Analysis, Vol. 1 (1998), pp. 109–124.
  • "Fractional Fourier transform of generalized functions," Journal of Integral Transforms and Special Functions, Vol. 7 No. 4(1998), pp. 299–312
  • "On the use of Green's function in sampling theory," (jointly with M. Annaby) Journal of Integral Equations and Applications, Vol. 10 (1998), pp. 117–139.
  • "New orthonormal sets and bases of the space of bandlimited functions", Proceedings of the International Conference on Sampling Theory and Applications, Aveiro, Portugal, June 1997.
  • "Sampling theorems associated with Dirac operator and the Hartley transform", (jointly with A. Garcia) the Journal of Math. Anal. Appls, Vol. 214 (1997), pp. 587–598.
  • "New orthogonal sets and frames in the Paley-Wiener space," Comptes Rendus Mathématiques de la Société Royale du Canada, Vol. 18, (1996), pp. 181–183
  • "Wavelet expansions of analytic hyperfunctions,"the Journal of Integral Transforms and Special Functions, Vol. 3 (1995), pp. 305-320.
  • "A generalized sampling theorem with the inverse of an arbitrary square summable sequence as sampling points, The Journal of Fourier Analysis and Applications, Vol. 2 (1996), pp. 303-314.
  • "Characterization of analytic functions in terms of their wavelet coefficients," (jointly with G. Walter), the Journal of Complex Variable: Theory and Applications, Vol. 29 (1996), pp. 265–276.
  • "On the extension of the Zak transform," (jointly with P. Mikusinski), The Journal of Methods and Applications of Analysis, Vol. 2 (1995),pp. 160–172.
  • "Sampling theorem for signals bandlimited to a general domain in several variables," Journal of Mathematical Analysis and Applications, Vol. 187, 1(1994), pp. 196–211.
  • "New summation formulas for multivariate infinite series by using sampling theorems," the Journal of Applicable Analysis, Vol. 54, 1(1994),pp. 135–150.
  • " Wavelet transforms of periodic generalized functions, "the Journal of Mathematical Analysis and Applications., Vol. 183, 2(1994), pp. 391-412.
  • "Sampling theorem for functions bandlimited to a disc," The journal of Complex Variables: Theory and Applications, vol. 26, 3(1994), pp. 245–254.
  • "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.
  • "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.
  • "A question on the existence of certain boundary-value problems," The Reviews of the Society for Industrial and Applied Mathematics (SIAM Rev.) Vol. 34 (1992), pp. 118–119.
  • "On the inversion of integral transforms associated with Sturm-Liouville problems," jointly with G. Walter, the 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, the Journal of Mathematical Analysis and Applications, Vol. 163, No. 1(1992), pp. 113–135.
  • On Lagrange interpolations and Kramer's sampling theorem associated with self-adjoint boundary-value problems," jointly with M. El-Sayed and M. Annaby, the Journal of Mathematical Analysis and Applications, Vol. 158, No. 1 (1991), pp. 269-284.
  • "On Kramer's sampling theorem associated with general Sturm-Liouville boundary-value problems and Lagrange interpolation," the Journal of Applied Mathematics of the Society for Industrial and Applied Mathematics., Vol. 51, No. 2 (1991), pp. 575–604.
  • "Generalized Faber expansions of hyperfunctions on analytic curves," the Journal of the Mathematical Society of Japan, Vol. 42, No. 1 (1990), pp. 155–170.
  • "On integral transforms whose kernels are solutions of singular Sturm-Liouville problems, Proceedings of the Royal Society of Edinburgh, 108A, (1988), pp. 201-228.
  • "Sampling expansions for the continuous Bessel transform," Journal of Applicable Analysis, Vol. 27 (1988), pp. 47–64.
  • "A generalized inversion formula for the continuous Jacobi transform when = 0," the International Journal of Mathematics and Mathematical Sciences., Vol. 10, No. 4 (1987), pp. 671–692.
  • "A generalized inversion formula for the continuous Jacobi transform," Mathematical Reports of the Canadian Academy of Science, Vol. 8, No. 4 (1986), pp. 271–276.
  • "Real singularities of Sturm-Liouville expansions" the Journal of Mathematical Analysis of the Society for Industrial and Applied Mathematics., Vol. 18, No. 1 (1987), pp. 219–227 (jointly with G. Walter).
  • "Complex and real singularities of eigenfunction expansions," Proceedings of the Royal Society of Edinburgh, Vol. 103A (1986), pp. 179–199.
  • "On the singularities of singular Sturm-Liouville expansions and an associated class of elliptic P.D.E.'s." the Journal of Mathematical Analysis of the Society for Industrial and Applied Mathematics., Vol. 16, No. 4 (1985), pp. 725–740 (jointly with G. Walter).
  • "Series of orthogonal polynomials as hyperfunctions," the Journal of Mathematical Analysis of the Society for Industrial and Applied Mathematics, Vol. 13, No. 4 (1982), pp. 664–675 (jointly with G. Walter).
  • "Laguerre series as boundary values," the Journal of Mathematical Analysis of the Society for Industrial and Applied Mathematics, Vol. 13, No. 2 (1982), pp. 263–279.

References
  1. Full Time Faculty Archived 2010-03-11 at the Wayback Machine, Department of Mathematical Sciences at DePaul University.
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