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Downloadable Publications

  1. Neural networks for optimal approximation of smooth and analytic functions; Neural Computation, {\bf 8} (1996), 164-177.  pdf
  2. Neural networks for functional approximation and system identification; Neural Computation, {\bf 9} (1997), 143–159. (With N. Hahm) pdf
  3. On Marcinkiewicz-Zygmund-Type Inequalities;  in “Approximation theory: in memory of A. K. Varma”, (N. K. Govil, R. N. Mohapatra, Z. Nashed, A. Sharma, and J. Szabados Eds.), Marcel Dekker 1998, pp.389–404. (With J. Prestin) pdf
  4. Polynomial frames for the detection of singularities; in  “Wavelet Analysis and Multiresolution Methods” (Ed. Tian-Xiao He), Lecture Notes in Pure and Applied Mathematics, Vol. 212, Marcel Decker, 2000, 273–298. (With J. Prestin).  pdf
  5. On a sequence of fast decreasing polynomials; in “Applications and computation of orthogonal polynomials” (W. Gautschi, G. Golub, M. Opfer Eds.), Internat. Ser. Numer. Math. Vol. 131, Birkhäuser, Basel, 1999, 165-178. (With J. Prestin). pdf
  6. On the detection of singularities of a periodic function; Advances in Computational Mathematics, {\bf 12} (2000), 95–131  (With J. Prestin). pdf
  7. Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Math. Comp. {\bf 70} (2001), no. 235, 1113–1130.  (With F. J. Narcowich and J. D. Ward). (Corrigendum: Math. Comp. {\bf 71} (2001), 453–454.) (In some publications, referred to as:
    Quadrature formulas on spheres using scattered data) pdf
  8. Approximation properties of zonal function networks using scattered data on the sphere; Advances in Computational Mathematics, {\bf 11} (1999), 121–137. (With F. J. Narcowich and J. D. Ward) pdf
  9. Polynomial frames on the sphere; Adv. Comput. Math. 13 (2000), no. 4, 387–403.  (With F. J. Narcowich, J. Prestin, and J. D. Ward). pdf
  10. Zonal function network frames on the sphere;  Neural Networks, {\bf 16}(2) (2003), 183–203 (With F. J. Narcowich and J. D. Ward). pdf
  11. Approximation theory and neural networks; in  “Wavelet Analysis and Applications, Proceedings of the international workshop in Delhi, 1999” (P. K. Jain, M. Krishnan, H. N. Mhaskar J. Prestin, and D. Singh Eds.), Narosa Publishing, New Delhi, India, 2001, 247–289. pdf
  12. On the representation of band limited functions using finitely many bits;  Journal of Complexity, {\bf 18} (2002), no. 2, 449–478. pdf
  13. On the degree of approximation in multivariate weighted approximation;  in “Advanced Problems in Constructive Approximation” (Proceedings of the IDOMAT 2001 conference) (M.D. Buhmann  and D.H. Mache  Eds.), ISNM {\bf 142}, Birkh\”auser, Basel, 2002, pp.129–141. pdf
  14. On the representation of band-dominant functions on the sphere
    using finitely many bits;  Advances in Computational Mathematics, {\bf 21} (2004), 127–146. (With F. J. Narcowich and J. D. Ward). pdf
  15. When is approximation by Gaussian networks necessarily a linear process?; Neural Networks, {\bf 17} (2004), 989–1001.
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  16. Local quadrature formulas on the sphere; Journal of Complexity, {\bf 20} (2004), 753–772. pdf
  17. On the tractability of multivariate integration and approximation by neural networks; Journal of Complexity, {\bf 20} (2004), 561–590. pdf
  18. Local quadrature formulas on the sphere, II; in “Advances in Constructive Approximation” (M. Neamtu and E. B. Saff  eds), Nashboro Press, Nashville, 2004, pp. 333–344. pdf
  19. On local smoothness classes of periodic functions; Journal of Fourier Analysis and Applications, {\bf 11} (3) (2005), 353 – 373  (with J. Prestin). pdf
  20. Polynomial operators and local smoothness classes on the unit interval; Journal of Approximation Theory, {\bf 131}(2004),  243-267. pdf
  21. On the representation of smooth functions on the sphere using finitely many bits; Applied and Computational Harmonic Analysis
    {\bf 18}, Issue 3 , May 2005, Pages 215-233. pdf
  22. A Markov–Bernstein inequality for Gaussian networks; in “Trends and applications in constructive approximation” (M. G. de Bruin, D. H. Mache, and J. Szabados eds.), ISNM {\bf 105}, Birkh\”auser Verlag, Bassel, 2005, pp. 165–180.  pdf  
  23. Polynomial frames: a fast tour; in “Approximation Theory XI, Gatlinburg, 2004” (C. K. Chui, M. Neamtu, and L. Schumaker Eds.), Nashboro Press, Brentwood, 2005, 287–318 (With J. Prestin). pdf
  24. On quasi–interpolatory polynomial operators; in “Frontiers in interpolation and approximation” (N. K. Govil, H. N. Mhaskar, R. N. Mohapatra, Z. Nashed, and J. Szabados eds.), Chapman and Hall/CRC, Boca Raton,  2006, pp. 345–364 (Invited paper). pdf
  25. Polynomial operators and local approximation of solutions of eudo-differential operators on the sphere; Numerische Mathematik, {\bf 103} (2006), 299–322 (with Q. T. Le Gia) pdf
  26. Matrix–free interpolation on the sphere; SIAM J. Numer. Analysis {\bf 44} (3) (2006), pp. 1314–1331 (With M. Ganesh) pdf
  27. Quadrature–free quasi–interpolation on the sphere; Electronic Transactions on Numerical Analysis,{\bf 25} (2006), 101–114 (With M. Ganesh) pdf
  28. Weighted quadrature formulas and approximation by zonal function networks on the sphere; Journal of Complexity Theory, {\bf 22} (3), June 2006, 348–370.
    pdf
  29. Quadrature in Besov spaces on the Euclidean sphere; {\bf 23} (2007), 528–552 (With K. Hesse and I. H. Sloan) pdf
  30. Quadrature formulas and localized linear polynomial operators  on the sphere; SIAM J. Numer. Anal. {\bf 47} (1) (2008), 440–466. (With Q. T. Le Gia) pdf
  31. Diffusion polynomial frames on metric measure spaces; Applied and Computational Harmonic Analysis, Volume 24, Issue 3, May 2008, Pages 329-353(With M. Maggioni). pdf
  32. Polynomial operators for spectral approximation of piecewise analytic functions; Appl. Comput. Harmon. Anal. {\bf 26} (2009) 121–142 (With J. Prestin) pdf
  33. Polynomial operators and local smoothness classes on the unit interval, II;  Ja\’en J. of Approx., {\bf 1} (1) (2009), 1–25.  (Invited paper) pdf
  34. On a filter for exponentially localized kernels based on Jacobi polynomials; Accepted  for publication in J. Approx. Theory. (With F. Filbir and J. Prestin) pdf
  35. Eignets for function approximation; Appl. Comput. Harmon. Anal. 29 (2010) 63–87 pdf
  36. A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel; Journal of Fourier Analysis and Applications  16 (2010), 629–657 (with F. Filbir) pdf
  37. Marcinkiewicz–Zygmund measures on manifolds; Journal of Complexity, {\bf 27} (2011), 568–596 (With F. Filbir) pdf