Recent research papers of faculty members of the Center for Constructive Approximation are listed below. Additional research papers are listed on members' individual websites.

Akram Aldroubi
  • Optimal Non-Linear Models for Sparsity and Sampling, (with C.A. Cabrelli and U.M. Molter) arxiv:0707.2008.
  • Slanted Matrices, Banach frames, and Sampling, (with I. Krishtal and A. Baskakov), arxiv:0705.4304.
  • On Stability of Sampling-Reconstruction Models, (with E. Acosta and I. Krishtal), arxiv:0705.4309.
  • Error Analysis of Frame Reconstruction from Noisy Samples, (with C. Leonetti and Q. Sun), IEEE Transaction Signal Processing, in press.
  • Non-uniform sampling and reconstruction from sampling sets with unkown jitter, (with Casey Leonetti), STSIP, in press.
  • Optimal Shift invariant spaces and their Parseval frame generators, (with C. Cabrelli, U. Molter and D. Hardin), Comp. Harm. Anal, 273-283, 2007.
  • Robustness of sampling and reconstruction and Beurling-Landau-type theorems for Shift-Invariant spaces, (with Ilya Krishtal), Special issue on Computational Harmonic Analysis, Appl. Comp. Harm. Anal., Vol. 20, 256-260, 2006.
  • Improved fiber tractography with Bayesian tensor regularization, (with Yonggang Lu, John C. Gore, Adam W. Anderson and Zhaohua Ding ), NeuroImage, 1061-1074, 2006.
  • Convolution, average sampling, and a Calderon resolution of the identity for shift-invariant spaces, (with Q. Sun, and W-S Tang), Journal of Fourier Analysis and Application, 216-244, 2005.
  • Learning the right model from the data, (with Carlos, Cabrelli, and Ursula Molter), accepted.

Doug Hardin
  • Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds, (with E. B. Saff), Advances in Math., Vol. 193, No. 1 (2005), pp. 174-204. PDF

Mike Neamtu
  • Discriminative common vector method with kernels, (with H. Cevikalp and M. Wilkes), submitted. PDF

Alex Powell
  • Gabor Schauder bases and the Balian-Low Theorem, (joint with C. Heil), Journal of Mathematical Physics, 47, 113506 (2007), 21 pages.
  • Uncertainty principles for orthonormal sequences, (joint with P. Jaming), Journal of Functional Analysis, 243 (2007), 611-630.
  • An optimal example for the Balian-Low uncertainty principle, (joint with J. Benedetto and W. Czaja), SIAM Journal on Mathematical Analysis, 38 (2006), 333-345.
  • Recent developments in the Balian-Low Theorem, (joint with W. Czaja), in Harmonic Analysis and Applications (edited by C. Heil), Birkhauser, Boston, 2006.
  • A (p,q) version of Bourgain's theorem, (joint with J. Benedetto), Transactions of the AMS, 358 (2006), 2489-2505.
  • Sigma-Delta quantization and finite frames, (joint with J. Benedetto and O. Yilmaz), IEEE Transactions on Information Theory, 52 (2006), 1990-2005.
  • An endpoint (1,infinity) Balian-Low Theorem, (joint with J. Benedetto, W. Czaja, J. Sterbenz), to appear in Mathematical Research Letters.
  • Second order Sigma-Delta quantization of finite frame expansions, (joint with J. Benedetto and O. Yilmaz), Applied and Computational Harmonic Analysis, 20 (2006), no. 1, 126--148.
  • Time-frequency mean and variance sequences of orthonormal bases, Journal of Fourier Analysis and Applications, 11 (2005), no. 4, 375--387.

Edward Saff
  • Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials, (with A.I. Aptekarev and V.A. Kalyagin), submitted. PDF
  • Asymptotics of Weighted Best-Packing on Rectifiable Sets, (with S. V. Borodachov and D. P. Hardin), submitted. PDF
  • The Support of the Limit Distribution of Optimal Riesz Energy Points on Sets of Revolution in R3­, (with J. Brauchart and D. Hardin), submitted. PDF
  • The Support of the Riesz Equilibrium Measure on Sets of Revolution in R3­, (with J. Brauchart and D. Hardin), submitted. PDF
  • Asymptotics of Orthogonal Polynomials with Respect to an Analytic Weight with Algebraic Singularities on the Circle, (with A. Martínez-Finkelshtein and K. T.-R. McLaughlin), International Mathematics Research Notices, Vol. 2006, pp. 1-43. PDF
  • Asymptotics for Polynomial Zeros: Beware of Predictions from Plots, (with N.S. Stylianopoulos), accepted for publication in Computational Methods and Function Theory. PDF
  • Asymptotics of Best-Packing on Rectifiable Sets, (with S.V. Borodachov and D.P. Hardin), Proceedings of the American Mathematical Society, Vol. 135 (2007), pp. 2369-2380. PDF
  • Riesz Spherical Potentials with External Fields and Minimal Energy Points Separation, (with P. Dragnev), Potential Analysis, Vol. 26, No. 2 (2007), pp. 139-162. PDF
  • The Support of the Logarithmic Equilibrium Measure on Sets of Revolution in R3, (with D. Hardin and H. Stahl), J. Math. Phys., Vol. 48, No. 2 (2007), 022901, 14 pp. PDF
  • Zero Distribution of Muntz Extremal Polynomials in Lp[0,1], (with D. Lubinsky), Proc. Amer. Math. Soc., Vol. 135 (2007), pp. 427-435. PDF
  • Asymptotics for Discrete Weighted Minimal Riesz Energy Problems on Rectifiable Sets, (with S.V. Borodachov and D.P. Hardin), accepted for publication in Trans. Amer. Math. Soc. PDF
  • 2-D Inverse Problems for the Laplacian: a Meromorphic Approximation Approach, (with L. Baratchart, F. Mandréa and F. Wielonsky), Journal de Mathématiques Pures et Appliqués, Volume 86, Issue 1, July 2006, Pages 1-41. PDF
  • A Remez-Type Theorem for Homogeneous Polynomials, ( with A. Kroo and M. Yattslev), Journal of the London Mathematical Society, Vol. 73, No. 2 (2006), pp. 783-796. PDF
  • On Separation of Minimal Riesz Energy Points on Spheres in Euclidean Spaces, (with A. B. J. Kuijlaars and X. Sun), Journal Comp. & Applied Math, Vol. 199, No. 1 (2007), pp. 172-180. PDF
  • Potential Theoretic Tools in Polynomial and Rational Approximation, (with A.L. Levin), in Harmonic Analysis and Rational Approximation, Vol. 327 (Fournier, Grimm, Leblond, Partington, Eds.), Springer, 2006, pp. 71-94. PDF
  • Szego Orthogonal Polynomials with respect to an Analytic Weight: Canonical Represenation and Strong Asymptotics, (with A. Martinez-Finkelshtein and K. T.-R. McLauglin), Constructive Approximation, Vol. 24, No. 3 (2006), pp. 319-363. PDF
  • Zero Distributions for Polynomials Orthogonal with Weights over Certain Planar Regions, (with E. Mina-Diaz and N.S. Stylianopoulos), Computational Methods and Function Theory, Vol. 5, No. 1 (2005), pp. 185-221. PDF

Larry Schumaker
  • Scattered data fitting on surfaces using projected Powell-Sabin splines, (with Oleg Davydov), in Mathematics of Surfaces 2007, R. Martin, M. Sabin, and J. Winkler (eds.), Springer, 2007, 138-153.
  • Interpolation and scattered data fitting on manifolds using projected Powell-Sabin splines, (with Oleg Davydov), IMAJNA, 2007.
  • Computing bivariate splines in scattered data fitting and the finite-element method, accepted for publication in Numerical Algorithms.
  • A local Lagrange interpolation method based on C1­ cubic splines on Freudenthal partitions, (with G. Hecklin, G. Nürnberger, and F. Zeilfelder), accepted for publication in Math. Comp.
  • Local Lagrange interpolation with cubic C1­ splines on tetrahedral partitions, (with G. Hecklin, G. Nürnberger, and F. Zeilfelder), accepted for publication in Journal of Approximation Theory.
  • A C1­ Quadratic Trivariate Macro-element Space Defined Over Arbitrary Tetrahedral Partitions, (with Tatyana Sorokina and Andrew J. Worsey), accepted for publication in Journal of Approximation Theory.
  • Bounds on the dimension of trivariate spline spaces, (with Peter Alfeld), accepted for publication in Advances in Computational Mathematics.
  • Trivariate Cr­ polynomial macro-elements, (with Ming-Jun Lai), Constr. Approx., Vol. 26 (2007), 11-28.
  • A C2­ trivariate macro-Element based on the Worsey-Farin split of a tetrahedron, (with Peter Alfeld), SIAM J. Num. Anal., 43 (2005), 1750-1765. PDF
  • A family of Cr­ Macro-elements on Powell-Sabin-12 splits, (with Tanya Sorokina), Math. Comp., 75 (2006) ,711-726.
  • Local Lagrange interpolation with bivariate splines of arbitrary smoothness, (with G. Nürnberger, V. Rayevskaya, and F. Zeilfelder), Constr. Approx., 23 (2006), 33-59. PDF
  • A C2­ trivariate macro-Element based on the Clough-Tocher split of a tetrahedron, (with Peter Alfeld), Comput. Aided Geom. Design 22 (2005), 710-721. PDF
  • A trivariate box macro-element, (with Tatyana Sorokina), Constr. Approx. Vol. 21, No. 3 (2005), 413-431.
  • A C2­ trivariate double-Clough-Tocher macro-element, (with Peter Alfeld), in Approximation Theory XI: Gatlinburg 2004, C. Chui, M. Neamtu, and L. L. Schumaker (eds), Nashboro Press (Brentwood), 2005, 1-14.
  • Two Lagrange interpolation methods based on C1­ splines on tetrahedral partitions, (with G. Nürnberger and F. Zeilfelder), in Approximation Theory XI: Gatlinburg 2004, C. Chui, M. Neamtu, and L. L. Schumaker (eds), Nashboro Press (Brentwood), 2005, 327-344.