Firdous A. Shah


Sr Assistant Professor | Ph. D ( J. M. I )
(Wavelet Analysis)

Department of Mathematics

Myself Dr. Firdous A. Shah, born and brought up in the place of springs namely Anantnag. I received my preliminary education from a nearby college and pursued my master’s and doctorate degrees from the University of Kashmir, Srinagar and  Jamia Millia Islamia,   New Delhi, respectively.  Presently, I am working as Assistant Professor in the Department of Mathematics, University of Kashmir, South Campus, India.  My primary research interests include basic theory of wavelets, wavelet packets, time-frequency analysis and applications of wavelets in mathematical modelling. So far, I have published more than 80 research articles in various international journals of high repute. In addition to this, I have co-authored three books on Wavelet Transforms and Their Applications

A.    Books Published

  • Lecture Notes on Wavelet Transforms, (with Lokenath Debnath), Birkhäuser, Springer, Boston, USA, 2017. ISBN 978-3-319-59432-3, ISBN 978-3-319-59433-0 (eBook).
  • Wavelet Transforms and Their Applications, (with Lokenath Debnath), Birkhäuser, Springer, New York, USA, 2015. ISBN 978-0-8176-8417-4, ISBN 978-0-8176-8418-1 (eBook).
  • Introduction to Wavelets with Applications, (with Khalil Ahmad), Real World Education Publishers, New Delhi-110025, India, 2013.  ISBN No. 978-81-927151-2-4.

B.    Selected Publications

  • F. A. Shah, Inequalities for nonuniform wavelet frames, Georgian Mathematical Journal, (2019),  (accepted). DeGruyter.
  • F. A. Shah and R. Abass, Solution of fractional oscillator equations using ultraspherical wavelets, International Journal of Geometric Methods in Modern Physics, accepted (2019), World Scientific.
  • H. M. Srivastava, F. A. Shah and R. Abass, An application of the Gegenbauer wavelet method for the numerical solution of the fractional Bagley-Torvik equation, Russian Journal of Mathematical Physics, 26(1) (2019), 77-93. Springer.
  • F. A. Shah, O. Ahmad and A. Rahimi, Frames associated with shift-invariant spaces on local fields, Filomat, 32(9) (2018), 3097-3110.
  • F. A. Shah and Azhar Y. Tantary, Quaternionic shearlet transform, Optik, 175 (2018), 115-125. Elsevier.
  • F. A. Shah, O. Ahmad and P. E. Jorgensen, Fractional wave packet systems in L^2(R), Journal of Mathematical Physics, 59 (2018), 073509.
  • F. A. Shah and L. Debnath, Fractional wavelet frames in L^2(R), Fractional Calculus and Applied Analysis, 21(2) (2018), 399-422. DeGruyter.
  • M. Rashidi-Kouchi, A. Rahimi and F. A. Shah, Duals and multipliers of controlled frames in Hilbert spaces, International Journal of Wavelets, Multiresolution and Information Processing, 16 (5) (2018), 1850057 (13 pages) World Scientific.
  • Y. Hamid, M. Sugumaran and F. A. Shah, Wavelet neural network model for network intrusion detection system, International Journal of Information Technology, (2018), (accepted). Springer. doi.org/10.1007/s41870-018-0225-x
  • F. A. Shah and Azhar Y. Tantary, Polar wavelet transform and the associated uncertainty principles, International Journal of Theoretical Physics, 57(6) (2018), 1774-1786. Springer.
  • O. Ahmad, F. A. Shah and N. A. Sheikh, Gabor frames on non-Archimedean fields, International Journal of Geometric Methods in Modern Physics, 15 (2018) (17 pages) 1850079, World Scientific.
  • F. A. Shah and O. Ahmad, Wave packet systems on local fields, Journal of Geometry and Physics, 120 (2017), 5-18. Elsevier.
  • F. A. Shah and R. Abass, An efficient wavelet based collocation method for handling singularly perturbed boundary-value problems in fluid mechanics, International Journal of Nonlinear Sciences and Numerical Simulations,  18(6) (2017), 7-25. DeGruyter.  
  • F. A. Shah, O. Ahmad and N. A. Sheikh, Orthogonal Gabor systems on local fields, Filomat, 31(16) (2017), 5193-5201.
  • F. A. Shah and M. Y. Bhat, Nonuniform wavelet packets local fields of positive characteristic, Filomat, 31(6) (2017), 1491-1505. Siberia. 
  • F. A. Shah, Periodic wavelet frames on local fields of positive characteristic, Numerical Functional Analysis and Optimization, 37(5) (2016), 603-627. Taylor and Francis.  
  • F. A. Shah and M. Y. Bhat, Semi-orthogonal wavelet frames on local fields, Analysis, 36(3) (2016), 173-182. DeGruyter. 
  • F. A. Shah and M. Y. Bhat, Construction of biorthogonal wavelet packets on local fields of positive characteristic, Turkish Journal of Mathematics, 40 (2016), 292-309.  Turkey. 
  • F. A. Shah and M.Y. Bhat, Vector-valued non-uniform multiresolution analysis on local fields, International Journal of Wavelets, Multiresolution and Information Processing, 13(4) (2015), Article ID: 1550029. 22 pages. World Scientific.
  • F. A. Shah and Abdullah, Nonuniform multiresolution analysis on local fields of positive characteristic, Journal of Complex Analysis and Operator Theory, 9(7) (2015), 1589-1608. Springer.
  • A. B. Dar and F. A. Shah, In search of leading indicator property of yield spread for India: An analysis based on quantile and wavelet regression, Economics Research International, (2015), Article ID: 308567, 12 pages, Hindawi.
  • F. A. Shah and Abdullah, Wave packet frames on local fields of positive characteristic, Applied Mathematics and Computations, 249 (2014), 133-141. Elsevier.
  • F. A. Shah and Abdullah, A characterization of tight wavelet frames on local fields of positive characteristic, Journal of Contemporary Mathematical Analysis, 49 (6) (2014), 251-259. Springer.
  • A. B. Dar and F. A. Shah, Are Euro-zone fixed income markets integrated? An analysis based on wavelet multiple correlation and cross-correlations, Economics Research International, (2014), Article ID 219652, 8 pages, Hindawi.
  • A. B. Dar, A. Samantaraya and F. A. Shah, The predictive power of yield spread: Evidence from wavelet analysis, Empirical Economics, 46 (2014), 887-901. Springer.
  • F. A. Shah, Tight wavelet frames generated by the Walsh polynomials, International Journal of Wavelets, Multiresolution and Information Processing, 11 (6) (2013), 15 pages. World Scientific, Singapore.
  • F. A. Shah and L. Debnath, Tight wavelet frames on local fields, Analysis, 33(3) (2013), 293-307. Germany. 
  • F. A. Shah, Gabor frames on a half-line, Journal of Contemporary Mathematical Analysis, 47(5) (2012), 251-260.Springer.
  • F. A. Shah and L. Debnath, Explicit construction of M-band framelet packets, Analysis, 32(4) (2012), 281-294. Germany.
  • F. A. Shah and L. Debnath, p-Wavelet frame packets on a half-line using the Walsh-Fourier transform, Integral Transforms and Special Functions, 22(12) (2011), 907-917. Taylor and Francis.
  • F. A. Shah and L. Debnath, Dyadic wavelet frames on a half-line using the Walsh-Fourier transform, Integral Transforms and Special Functions, 22(7) (2011), 477-486. Taylor and Francis.
  • F. A. Shah and Abdul Wahid, Wavelet packets on locally compact Abelian groups, Analele Stiintifice ale Universitatii Ovidius, Seria Matematica (ASUOC), 18 (2) (2010), 223-240. Romania.
  • F. A. Shah, Construction of wavelet packets on p-adic fields, International Journal of Wavelets, Multiresolution and Information Processing, 7 (5) (2009), 553-565. World Scientific Singapore.