**Below are samples of my publications in these areas,
for a full list of publications, click here.**

1) “ Sampling of signals bandlimited to a disc in the linear canonical transform domain” IEEE Signal Processing Letters, Vol. 25 (2018), pp. 1765-1769.

2) “ On Sampling Theorems for Fractional Fourier Transforms and Series,” &ldquo ** Proceedings of the SampTa 17, the 12th International Conference on Sampling Theory and Applications, Tallinn, Estonia ** 2017, appeared digitally on IEEE Xplore Digital Library,

3) “ Shift-invariant and Sampling Spaces Associated with the Special Affine Fourier Transform ” (jointly with A. Bhandari), ** journal of Applied and Computational Harmonic Analysis **(to appear)

4) . “*New Perspectives on Approximation and Sampling Theor**y*” (A. Zayed and G. Schmeisser, Editors), Bikhauser, 2015.

5) Shift-invariant and Sampling Spaces Associated with the Fractional Fourier
Transform Domain, ** IEEE Transactions on Signal Processing**, Vol. 60, No. 3, 2012,
pp. 1627-1637 (jointly with A. Bhandari.).

6) Sampling Theorem for Bandlimited Hardy Space Functions Generated by Regge
Problem, ** Applied and Computational Harmonic Analysis**, Vol. 31 (2011), pp. 125-142
(jointly with M. Shubov).

7) On the Notion of Bandlimitedness and its Generalizations, ** Journal of the
Argentinean Mathematical Society, Revista De La Union Matematica Argentina, **
Vol. 49 (2008) pp. 99-109.

8) “Sampling expansions of functions having values in a Banach space,” ** Proceedings of the American Mathematical Societ**, Vol. 133, # 12 (2005), pp.
3597- 3607 (jointly with D. Han).

9) “A q-analogue of the Whittaker-Shannon-Kotel’nikov Sampling
theorem, ** Proceedings of the American Mathematical Societ**, Vol. 131, pp. 3711-3719
(2003), (jointly with M. Ismail).

10) “ 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.

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

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

13) “ Kramer's sampling theorem for multidimensional signals and its
relationship with Lagrange-type interpolation,"** Journal of multidimensional systems and signal processing**, Vol. 3 (1992), pp. 323-340.

1) “The continuous wavelet transform,” ** Standard Mathematical Tables and Formulae, 33rd Edition,** CRC Press (2017).

2) “Wavelets: Continuous Transform and Series,” **Encyclopedia of Optical and Photonic Engineering**, Second Edition, August 30, 2015. http://www.taylorandfrancis.com/books/details/9781439850978

3) Preface to Multi-scale Analysis,”** Multi-scale Analysis and Modeling**, Research Monograph:, Springer-Verlag, 2012

*4) “Wavelets, Multiscale Analysis, and Their Applications*: An Introduction, Chapter 1,” in **Wavelets and Multiscale Analysis**, J. Cohen and Ahmed Zayed, Editors; Birkhauser Publishing February 2011

5) Shift-invariant and Sampling Spaces Associated with the Fractional Fourier Transform Domain, IEEE Transactions on Signal Processing, Vol. 60, No. 3, 2012, pp. 1627-1637 (jointly with A. Bhandari.),

6) “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), Jointly with L. Dettori,.

7) “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).

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

9) 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.

10) “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..

11) "Pointwise convergence of a class of non-orthogonal wavelet expansions,"
*Proceedings of the American Mathematical Society*, Vol. 128 (2000),
pp. 3629-3637.

1) “ A new perspective on the role of mathematics in medicine ” Journal of Advanced Research, Elsiever Publications (to appear 2019).

2) “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).

3) 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).

1) “ Two-dimensional Fractional Fourier Transform and Some of its Properties ” **J. Integral Transforms and Special functions,** Vol. 29-7 (2018), pp. 553-570.

2) “ A New Perspective on the Two-Dimensional Fractional Fourier Transform and its Relationship with the Wigner Distribution ” ** Journal of Fourier Analysis and Applications, **Vol. 25-2 (2019), pp. 460-487.

3) "On Sampling Theorems for Fractional Fourier Transforms and Series,” ** Proceedings of the SampTa 17, the 12th International Conference on Sampling Theory and Applications, ** Tallinn, Estonia (2017).

4) “On the Invalidity of Fourier Series Expansions of Fractional Order” **J. Fractional Calculus and Applied Analysis**, Vol. 18, No. 6 (2015) pp. 1507-1517 (jointly with P. Massupost).

5) Shift-Invariant and Sampling Spaces Associated with the Fractional Fourier Transform Domain, (jointly with A. Bhandari.), ** IEEE Transactions on Signal Processing**, Vol. 60, No. 3, (2012), pp. 1627-1637.

6) “ Fractional Wigner distribution and ambiguity functions,” (jointly
with V. B. Shakhmurov) ** J. Fractional Calculus and Applied Analysis**,
Vol. 6. No. 4 (2003), pp. 473-490

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

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

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

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

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

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

13) " 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.

1) “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)

2) “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).

3) “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 withM. El-Gamel).

4) “A Comparison between the wavelet-Galerkin and the Sinc-Galerkin methods
in solving non-homogeneous heat equations,”*Contemporary Mathematics***, American Mathematical Society, **Vol. 313 (2002), pp. 97-116. (Jointly with M. El Gamel),

1) “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.

2) “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.

3) “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 .

40 "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.

1) “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).

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

3) "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).

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

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

1) “Linear Transformations in Signal and Optical Systems,” **Handbook of Operator Theory**, D. Alpay, Editor, Springer-Verlag, (2015), P. 833-874.

2) Paley-Wiener Subspace of Vectors in a Hilbert Space with Applications to Integral Transforms, **Journal of Mathematical Analysis and Applications**, Vol. 353 (2009), pp. 566-582. (jointly with I. Pesenson)

3) "On the extension of the Zak transform," (jointly with P. Mikusinski),
* Journal of Methods and Applications of Analysis*, Vol. 2 (1995),pp. 160-172.

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

5) "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.

6) "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.

1) "On the theta semi-group," journal of Complex Analysis and Operator Theory, (2012) 6: 565-583 (jointly with W. Urbina),.

2) "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.

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

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

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

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

1) Chromatic Expansions in Function Spaces, ** Transactions of the American Mathematical Society**, Vol. 366, No. 8, (2014), pp. 4097-4125.

2) “*Chromatic Expansions and the Bargman Transform*,” Chapter 6 in **Multi-scale Analysis and Modeling**, Research Monograph, (Xiaoping Shen and Ahmed Zayed, Editors), Springer-Verlag, 2012.

3) Chromatic Expansions in Reproducing-kernel Hilbert Spaces, Progress in Analysis, **Proceedings of the 8th ISAAC Congress, Moscow, Russia, 2011**, People’s Friendship University of Russia, Publisher (2012), pp. 346-355.

4) "Multidimensional chromatic derivatives and series expansions,"
(jointly with A. Ignjatovic) **Proceedings of the American Mathematical Society**,
Vol. 139, No. 10 (2011), pp. 3513-3525.

5) "Chromatic derivatives of generalized functions," **Journal of
Integral Transforms and Special Functions**, Vol. 22, No. 4-5 (2011), pp. 383-390.

6) "Generalizations of Chromatic Derivatives and Series Expansions,"
(Institute of Electrical and Electronics Engineers) **IEEE Transactions on Signal
Processing, **Vol. 58, No. 3, (2010), pp. 1638- 1647.

1) “Numerical Solution to an Energy Concentration Problem Associated with the Special Affine Fourier Transformation,” (jointly with Amara Ammari and Tahar Moumni), ** Frames and other Bases in Abstract and Function Spaces, ** I. Pesenson, et al Editors, Birkhauser (2017),pp. 161-184

2) The Prolate Spheroidal Wave Function,” ** Standard Mathematical Tables and Formulae, 33rd Edition, ** CRC Press (2017).

3) Maximally concentrated signals in the special affine Fourier transformation domain, **Proceedings of 2015 International Conference on Sampling Theory and Applications (SampTA) July 2015**, http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7148841.

4) Solution of the Energy Concentration Problem in Reproducing-Kernel Hilbert Space,** Journal of the Society for Industrial and Applied Mathematics (SIAM) on Applied Mathematics**, Vol. 75, No. 1 (2015), pp. 21-37.

5) A Generalization of the Prolate Spheroidal Wave Functions with Applications to Sampling (jointly with Taher Moumni),** Journal of Integral Transforms and Special Functions**, Vol. 25, No. 6, (2014), pp. 433-447.

6) A Generalization of the Prolate Spheroidal Wave Functions,” ** Proceedings of the American Mathematical Society**, Vol. 135, (2007), pp. 2193-2203.

1) ** Topics in Harmonic Analysis and Ergodic Theory**,” Contemporary Mathematics Series, American Mathematical Society, Volume 444, (2007), J. Rosenblatt, A. Stokolos, and A. Zayed, Editors.

2) The Zak transform," **Encyclopedia of Mathematics**, Supplement III, Kluwer Publications, 2001.

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