Publications

Books

1. “Sampling, Wavelets, and Tomography,” Co-Editor with J. Benedetto, Birkhauser, Boston , 2003.

2. “Function and Generalized Function Transformations" CRC Press, Boca Raton, Florida, 1996.

3. "Mathematical Analysis, Wavelets and Signal Processing," American Mathematical Society,
Contemporary Mathematics Series, Vol. 190 (1995), Co-Editor with M. Ismail, and Z. Nahsed.

4. "Advances in Shannon's Sampling Theory," CRC Press, Boca Raton, Florida, 1993.

Chapters in Books and Encyclopedia:

1. “A Prelude to Sampling, Wavelets, and Tomography,” Chapter 1 in Sampling, Wavelets, and Tomography, A.I Zayed and J. Benedetto, Editors, Birkhauser.

2. Chapter on "Wavelets," Encyclopedia of Optical Engineering, Marcel Dekker.

3. " The Zak transform," Encyclopedia of Mathematics, Supplement III, Kluwer Publications

4. “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.

5. “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.

6. “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..

7. "Integral Transforms," 30th Edition of "CRC Standard Tables and Formulae," CRC Press, Boca Raton, FL (1995).

Papers:

1. “Sampling expansions of functions having values in a Banach space,” (jointly with D. Han), to appear in the Proceedings of the American Mathematical Society.

2. “Sampling theorems, Lagrange interpolation, and boundary-value problems,” (jointly with C. Shin), submitted.

3. 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.

4. “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.

5. “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.

6. “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).

7. “Sinc-Galerkin method for solving linear sixth order boundary-value problems,” Mathematics of Computation, American Mathematical Society, (jointly with M. El-Gamel and J. Cannon), Vol. 73, No. 247 (2004), pp. 1325-1343 .

8. “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.

9. “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).

10. “Construction of orthonormal wavelets using Kampe de Feriet functions," the Proceedings of the American Mathematical Society, Vol. 130 (2002), pp.2893-2904.

11. “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.

12. "Sampling on a string," (jointly with A. Boumenir), The Journal of Fourier Analysis and
Applications, Vol. 8 (2002), pp. 211-231.

13. On the Lame series representation of analytic hyperfunctions on a two-dimensional complex
manifold,” in “Micro-local Analysis and Complex Fourier Analysis, Editors, K. Fujita and M. Morimoto,
World Scientific Publisher (2002), pp. 317-328.

14. “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.

15. “Density deconvolution of different conditional distributions,” (jointly with M. Pensky), Annals of the Institute of Statistical Mathematics, Vol. 54 (2002), pp. 701-712.

16. “A class of fractional integral transforms: A generalization of the fractional Fourier transform,” IEEE Transactions on Signal Processing, Vol. 50 (2002), pp. 619-627.

17. “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..

18. " 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.

19. “Generalization of a theorem of Boas to a class of integral transforms,” (jointly with V. k. Tuan), the
Jorunal of Resultät der Mathematik. Vol. 38 (2000), pp. 362-376.

20. “Paley-Wiener-type theorem for a class of integral transforms arising from a singular Dirac system,” (jointly with V. k. Tuan), “Zeitschrift für Analysis und ihre Anwendungen,”Vol. 19 (2000), pp. 695-712.

21. "Pointwise convergence of a class of non-orthogonal wavelet expansions," Proc. Amer. Math. Soc., Vol. 128 (2000), pp. 3629-3637.

22. “New Sampling Formulae for the Fractional Fourier Transform,” (jointly with A. Garcia) the Journal of Signal Processing, Vol. 77 (1999), pp. 111-114.

23. "Kramer's sampling theorem with discontinuous kernels," (jointly with A, Garcia), Resultät der Mathematik, Vol. 34 (1998), pp. 197-206.

24. "B-spline wavelets and orthonormal sets in the Paley-Wiener space," “Analysis of Divergence: Control and Management of Divergent Processes,” W. Bray and C. Stanojevic, Editors, Birkhauser, Boston (1999).

25. "Multiresolution analysis with sampling subspaces," (jointly with G. Walter), Journal of Fractional Calculus and Applied Analysis, Vol. 1 (1998), pp. 109-124.

26. “Hilbert transform associated with the fractional Fourier transform,” IEEE Signal Proc. Letters, Vol 5, No 8 (1998), pp. 206-208.

27. "A convolution and product theorem for the fractional Fourier transform," IEEE Signal Processing Letters, Vol. 5, No. 4 (1998), pp. 101-103.

28. "Fractional Fourier transform of generalized functions," Journal of Integral Transforms and Special Functions, Vol. 7 No. 4(1998), pp. 299-312.

29. "Sampling expansions associated with boundary-value problems and orthonormal bases of the Paley-Wiener space," the Journal of Communications in Applied Analysis, Vol. 3 (1999), pp. 85-99.

30. "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.

31. "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.

32. "Non-uniform sampling of bandlimited signals with polynomial growth on the real axis," (jointly with A. Garcia) IEEE Trans. Inform. Theory, Vol. 43, 5 (1997), pp. 1717-1721.

33. "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.

34. "On the relationship between the Fourier and fractional Fourier transforms," IEEE Signal Processing Letters, Vol. 3 (1996), pp. 310-311.

35. "New orthogonal sets and frames in the Paley-Wiener space," Comptes Rendus Mathematiques, de la Société Royale du Canada, Vol. 18, (1996), pp. 181-183.

36. "Sampling in a Hilbert Space," Proceedings of the American Mathematical Society, Vol. 124, (1996), pp. 3767-3776.

37. "Wavelet expansions of analytic hyperfunctions,"the Journal of Integral Transforms and Special Functions, Vol. 3 (1995), pp. 305-320.

38. "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.

39. "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.

40. "A generalization of Kramer's sampling theorem," Proceedings of an International Conference on Sampling Theory & Applications, Jurmala, Latvia, September, 1995.

41. "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.

42. "Centroid: Fourier transform versus wavelets," (jointly with Y. Gordon), Contemporary Mathematics, Amer. Math. Soc., Vol 190 (1995), pp. 127-141.

43. "Sampling theorems associated with boundary-value problems," the Proceedings of the Fourth International Colloquium on Differential Equations, Plovdiv, 1993, D. Bainov and V. Covachev, Editors, VSP International Science Publishers, Utrecht, The Netherlands, 1994, pp. 295-305.

44. "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.

45. "New summation formulas for multivariate infinite series by using sampling theorems," the Journal of Applicable Analysis, Vol. 54, 1(1994),pp. 135-150.

46. " Wavelet transforms of periodic generalized functions, "the Journal of Mathematical Analysis and Applications., Vol. 183, 2(1994), pp. 391-412.

47. "Sampling theorem for functions bandlimited to a disc," The journal of Complex Variables: Theory and Applications, vol. 26, 3(1994), pp. 245-254.

48. "An extension of the Radon Transform," (jointly with P. Mikusinski) "Generalized Functions and Their Applications", R.S. Pathak, editor, Plenum Press, New York (1993), 141- 147.

49. "Radon transform of Boehmians," (jointly with P. Mikusinski), Proceedings of the American Mathematical Society, Vol. 118 (1993), pp. 561-570.

50 . "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.

51. "A proof of new summation formulae by using sampling theorems," Proceedings of the American Mathematical Society, Vol. 117, No. 3 (1993), pp. 699-710.

52. "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.

53. "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).

54. "Generalized Jacobi transforms," jointly with E. Deeba, the Journal of Applicable Analysis., Vol. 48 (1993), pp. 63-79.

55. "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.

56. "On sampling theorems and the Gauss-Jacobi mechanical quadrature," The Mathematical Heritage of C.F. Gauss, edited by G. Rassias, World Sci. Publ.(1990).

57. "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.

58. "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.

59. "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.

60 . "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.

61. "On Lagrange interpolation and Kramer-type sampling theorems associated with regular Sturm?Liouville problems," jointly with P. Butzer and G. Hinsen, the Journal of Applied Mathematics of the Society for Industrial and Applied Mathematics., Vol. 50, No. 3 (1990), pp. 893-909.

62. "Jacobi polynomials as generalized Faber polynomials," Transactions of the American Mathematical Society, Vol. 321, No. 1 (1990), pp. 363-378.

63. "Generalized Faber expansions of hyperfunctions on analytic curves," the Journal of the Mathematical Society of Japan, Vol. 42, No. 1 (1990), pp. 155-170.

64. "The continuous Jacobi transform and its inverse when + 1 is a positive integer," Transactions of the American Mathematical Society, (jointly with G. Walter), Vol. 305, 2 (1988), pp. 653-664.

65. "On integral transforms whose kernels are solutions of singular Sturm-Liouville problems, Proceedings of the Royal Society of Edinburgh, 108A, (1988), pp. 201-228.

66. "A theorem of Nehari revisited," The Journal of complex variables, theory and applications, (jointly with Freund and Gorlich), Vol. 10, (1988), pp. 11-22.

67. "Sampling expansions for the continuous Bessel transform," Journal of Applicable Analysis, Vol. 27 (1988), pp. 47-64.

68. "A generalized inversion formula for the continuous Jacobi transform when + 1 is an integer," Proceedings of the International Conference on Orthogonal Polynomials, Segovia, Spain (1986), Monografias de la Academia de Ciencias de Zaragoza, No. 1 (1988), pp. 157-164.

69. "Inversion of an integral transform related to a general form of heat equation" the Journal of Mathematical Analysis and Applications (jointly with D. Haimo), Vol. 131, 1 (1988), pp. 246-264.

70. "On the singularities of the continuous Jacobi transform when = 0," Proceedings of the American Mathematical Society., Vol. 101, No. 1 (1987), pp. 67-75.

71. "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.

72. "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.

73. "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).

74. "Complex and real singularities of eigenfunction expansions," Proceedings of the Royal Society of Edinburgh, Vol. 103A (1986), pp. 179-199.

75. "On the singularities of continuous Legendre transforms'. Proceedings of the American Mathematical Society, Vol. 97, No. 4 (1986), pp. 673-681 (jointly with G. Walter).

76. "On the Poisson and the conjugate Poisson kernels for an annulus" Tamkang Journal of Mathematics, Vol. 17, No. 3 (1986), pp. 69-81.

77. "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).

78. "On the singularities and asymptotic expansions of singular Sturm-Liouville expansions," Ordinary and Partial Differential Equations, B. Sleeman and R. Jarvis, Editors, Proc. International Conference, Dundee, Scotland, Springer-Verlag Lectures Notes, Vol. 1151 (1985), pp. 350-357.

79. "Generalized functions and orthogonal polynomials on the unit circle," Proceedings of the American Mathematical Society, Vol. 88, No. 3(1983), pp. 407-415.

80. "Topological vector spaces of analytic functions," Journal of Complex Variables: Theory and Applications, Vol. 1, No. 4 (1983), pp. 27-50.

81. "Recoverability of some classes of analytic functions from their boundary values," Proceedings of the American Mathematical Society, , Vol. 87, No. 3 (1983), pp. 493-498.

82. "Asymptotic expansions of some integral transforms by using generalized functions," Transactions of the American Mathematical Society, , Vol. 272, No. 2 (1982), pp. 785-802.

83. "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).

84. "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.

85. "On Laguerre series expansions of entire functions," Tamkang Journal of Mathematics, Vol. 12, No. 1 (1981), pp. 39-45.

86. "Hyperfunctions as boundary values of generalized axially symmetric potentials," Illinois Journal of Mathematics, Vol. 25, No. 2 (1981), pp. 306-317.

87. "On the singularities of ultraspherical expansions," Transactions of the American Mathematical Society, Vol. 262, No. 2 (1980), pp. 487-503.

88. "Distributional derivatives and Abel summability of ultraspherical expansion," Real Analysis Exchange, Vol. 5, No. 1 (1979-1980), pp. 151-157.

89. "Two general theorems concerning Pade approximation," Proceedings of the Mathematical and Physical Society of Egypt, Vol. 39, No. 11 (1975) (jointly with A. B. Khalil).

90. "Pade approximation for the Coulomb interactions," Proceedings of the Mathematical and Physical Society of Egypt, Vol. 39, No. 11 (1975) (jointly with A. B. Khalil).

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