Publications

  1. Determination of the spectral gap in the Kac model for physical momentum and energy conserving collisions (with Eric Carlen and Michael Loss) SIAM Journal of Math Anal. 40 (2008) 327-364
  2. Varying weights for orthogonal polynomials with monotonically varying recurrence coefficients (with Walter Van Assche and Alexander Aptekarev) JAT 150 (2007) 214-238
  3. Two variable orthogonal polynomials on the bicircle and structured matrices (with Hugo Woerdeman) SIAM J Matrix Anal. Appl. 29 (2007) 796-825
  4. Two Variable polynomials Intersecting zeros and stability (with H Woerdeman) IEEE Trans Circuits and Systems 53 (2006) 1130-1139
  5. Two variable orthogonal polynomials and structured matrices (with A. Delgado, P. Iliev, and F. Marcellan) SIAM J. Matrix Anal. 28 (2006) 118-114
  6. Factorization of multivariate positive Laurent polynomials (with M-J Lai) JAT 139 (2006) 327-345
  7. On extensions of a Theorem of Baxter (with A. Martinez-Finkelstein) JAT 139 (2006) 214-222
  8. The Operator Valued Autoregressive Filter Problem and the Suboptimal Nehari Problem in Two Variables (with Hugo Weordeman) Integral Equations and Operator Theory 53 (2005) 343-361
  9. Asymptotics for Sobolev Orthogonal Polynomials for Exponential Weights(with D. Lubinsky and P. Marcellan) Const. Appr. 22 (2005) 309-346
  10. Algebro-Geometric Solutions of the Baxter-Szego Difference Equation (with F. Gesztesy and H. Holden) CMP 258 (2005) 149-177
  11. Positive extensions and Fejer-Riesz factorization for two-variable trigonometric polynomials (with H. Woerdeman) Annals of Math. 160 (2004) 839-906
  12. WKB and Turning Point Theory for Second Order Difference Equations (with O Bruno, and W. Van Assche) Operators Theory: Advances and Applications, 154 (2004) 101-138
  13. A Numerical Algorithm for the 2D Autoregressive Filter Problem (with H. Woerdeman and G. Castro) IEEE Transactions in Signal Proc. 83 (2003) 1299-1308
  14. Certain Two Dimensional Integrals that Appear in Conformal Field Theory (with H. Navelet) J. Math Physics, 44 (2003) 2293-2319
  15. Necessary and Sufficient Condition that the Limit of Stieljes Transforms is a Stieljes Transform (with T.P Hill) Journ. Approx. Theory 121 (2003) 54-60
  16. Squeezable Orthogonal Bases: Accuracy and Smoothness (with G. Donovan and D. Hardin) SIAM J. Numer. Anal. 40 (2002) 1077-1096
  17. Compactly Supported, Piecewise Affine Scaling Functions on Triangulations (with G.Donovan and D. Hardin) Const. Approx. 16 (2000) 201-219
  18. Orthogonal Polynomials and the Construction of Piecewise Polynomial Smooth Wavelets (with G. Donovan and D. Hardin) SIAM J. Math. Anal. 30 (1998) 1029-1056
  19. An Inverse Problem Associated with Polynomials Orthogonal on the Unit Circle (with R. Johnson) Commun. Math Phys. 193 (1998) 125-150
  20. The Inverse Fractal Problem for Polyhulled Disjoint Attractors (with A. Delui and R. Shonkwiler) Phil. Trans. R. Soc. Lond A 355 (1997) 1017-1062
  21. Design of Prefilters for Discrete Multiwavelet Transforms (with X. Xia, D. Hardin and B. Suter) IEEE Trans. Signal Proc. 44 (1996) 25-35
  22. Construction of orthogonal wavelets using fractal interpolation functions (with G. Donovan, D. Hardin and P. Massopust) SIAM J. Math. Anal. 27 (1996) 1158-1192
  23. Interwining multiresolution analysis and the construction of piecewise polynomial wavelets (with G. Donovan, and D. Hardin) SIAM J. Math. Anal. 27 (1996) 1791-1815
  24. Rotation Number Associated with Polynomials Orthogonal on the Unit Circle (with R. Johnson) JDE 132 (1996) 140-178
  25. Fractal functions and wavelet expansions based on several scaling functions (with D. Hardin and P. Massopust) J. Approx. Theory 78 (1994) 373-401
  26. Scattering Theory, Orthogonal Polynomials and Q-series, SIAM J. Math. Anal. 25 (1994) 392-419
  27. A Difference Equation Arising from the Trignometric moment Problem having Random Reflection Coefficients – An Operator Theoretic Approach (with A. Teplyaev) J. Funct. Anal 123 (1994) 12-45
  28. Strong Asymptotics for Orthogonal Polynomials with Regularly and Slowly Varying Recurrence Coefficients (with D. Smith and W. Van Assche) J. Approx. Theory 72 (1993) 141-158
  29. Fractal Interpolation Surfaces with an Application to a Two-Dimensional Multiresolution Analysis (with D. Hardin), J. Math Anal. and App. 176 (1993) 561-586
  30. Singularity Spectrum for Recurrent IFS Attractors (with J. F. King) Nonlinearity 6 (1992) 337-348
  31. WKB (Louisville-Green) Analysis of Second Order Difference Equations and Applications (with D. Smith) J. Approx. Theory 69 (1992) 269-301
  32. Approximating the weight function for orthogonal polynomials on several intervals (with W. Van Assche) J. Approx. Theory 65 (1991) 341-371
  33. Dimensions associated with recurrent self-similar sets (with A. Deliu, D. Hardin and R. Shonkwiler), Math. Proc. Camb. Phil. Soc. 110 (1991) 327-336.
  34. On Geometric Sequences of Reflection Coefficients (with D. S. Mazel and M. H. Hayes) IEEE Trans. on Accoustics, Speech, and Signal Processing 38 (1990) 1810-1812
  35. Relative Asymptotics for Orthogonal Polynomials with Unbounded Recurrence Coefficients (with W. Van Assche) J. Approx. Theory 62 (1990) 47-69
  36. Capacities of Measures Associated with Iterated Function Systems (with D. Hardin) Const. Approx. 5 (1989) 89-98
  37. Asymptotics for Orthogonal Polynomials with Unbounded Recurrence Coefficients (with W. Van Assche), Rocky Mountain J. Math. (19) (1989) 39-49
  38. Invariant Measures for Markov Processes Arising from Iterated Function Systems with Place Dependent Probabilities (with M. F. Barnsley, S. Demko, and J. Elton) Ann. Inst. Henri Poincare 24 (1988) 367-394
  39. Orthogonal Polynomials on Several Intervals via a Polynomial Mapping (with W. Van Assche) Trans. Amer. Soc. 308 (1988) 559-581
  40. Asymptotics for Orthogonal Polynomials On and Off the Essential Spectrum (with W. Van Assche) J. Approx. Theory. 55 (1988) 220-231
  41. On the Asymptotic Distribution of Eigenvalues of Banded Matrices (with E. M. Harrell II and W. Van Assche) Const. Approx. 4 (1988) 403-417
  42. Function Weighed Measures and Orthogonal Polynomials on Julia Sets (with D. Bessis and P. Moussa) Const. Approx. 4 (1988) 157-173
  43. On the Spectra of Infinite Dimensional Jacobi Matrices, J. Approx. Theory 53 (1988) 251-265
  44. Orthogonal Polynomials with Asymptotically Periodic Recurrence Coefficients (with W. van Assche) J. Approx. Theory 46 (1986) 251-283
  45. Almost Periodic Operators Associated with Julia Sets (with M. F. Barnsley and A. N. Harrington) Comm. Math. Phys. 99 (1985) 303-317 
  46. Geometry and Combinatorics of Julia Sets of Real Quadratic Maps (with M. F. Barnsley and A. N. Harrington) J. Stat. Phys. 37 (1984) 51-92 
  47. Ensembles de Julia et Proprietes de Localisation des Families Iterees D’Entiers Algebriques(with D. Bessis and P. Moussa) Comptes-Rendus (Paris) 299 (1984) 281-284
  48. Mellin Transforms Associated with Julia Sets and Physical Applications (with D. Bessis and P. Moussa) J. Stat. Phys. 34 (1984) 75-110
  49. Geometrical and Electrical Properties of Some Julia Sets (with M. F. Barnsley and A. N. Harrington) “Classical and Quantum Models and Arithmetic Problems” (ed. D. Chudnovskyand G. Chudnovsky) lecture notes pure and applied mathematics, Decker 92 (1984) 1-68 
  50. Geometry, Electrostatic Measure, and Orthoqonal Polynomials on Julia Sets for Polynomials (with M. F. Barnsley and A. N. Harrington) J. of Ergodic Theory and Dynamical Systems 3 (1983) 509-520
  51. Complex Spectral Dimensionality on Fractal Structures (with D. Bessis and P. Moussa) J. Physique.-Lett. 44 (1983) 977-982
  52. Some Tree-like Julia Sets and Pade Approximants (with M. F. Barnsley and A. N. Harrington) Lett. Math. Phys. 7 (1983) 279-286
  53. Infinite Dimensional Jacobi Matrices Associated with Julia Sets (with M. F. Barnsley and A. N. Harrington) Proc. Am. Math. Soc. 88 (1983) 625-630
  54. Necessary and Sufficient Conditions Relating the Coefficients in the Recurrence Formula to the Spectral Function for Orthogonal Polynomials (with P. G. Nevai) SIAM J. Math. Anal. 14 (1983) 622-637
  55. On the Invariant Sets of a Family of Quadratic Maps (with M. F. Barnsley and A. N. Harrington) Comm. Math. Phys. 88 (1983) 479-501
  56. Orthogonal Polynomials Associated with Invariant Measures on Julia Sets (with M. F. Barnsley and A. N. Harrington) Bull. Amer. Math. Soc. 7 (1982) 381-384
  57. Scattering Theory and Matrix Orthogonal Polynomials on the Real Line, Circuits Systems Signal Process I (1982) 471-495
  58. An Upper Bound on the Number of Eigenvalues of an Infinite Dimensional Jacobi Matrix, J. Math. Phys. 23 (1982) 917-921
  59. Matrix Orthogonal Polynomials on the Unit Circle, J. Math. Phys. 22 (1981) 1359-1365
  60. A Relation Between the Coefficients in the Recurrence Formula and the Spectral Function for Orthogonal Polynomials, Trans. Amer. Math. Soc. 260 (1980) 65-82
  61. Scattering Theory and Polynomials Orthogonal on the Real Line (with K. M. Case) Trans. Amer. Math. Soc. 258 (1980) 467-494
  62. Szego’s Theorem on Hankel Determinants, J. Math. Phys. 20 (1979) 484-491
  63. Scattering Theory and Polynomials Orthogonal on the Unit Circle (with K. M. Case) J. Math. Phys. 20 (1979) 299-320
  64. Circadian Rhythm: a Population of Interacting Neurons (with J. W. Jacklet) Science (1971) 74-79

(b) Accepted for Publication:

(c) Submitted for Publication:

REFEREED CONFERENCE PROCEEDINGS:

  • Two variable defomations or the Chebyshev measure (with Plamen Iliev) Accepted in Comtemporary Math contributed refereed paper
  • Asymptotics of q-difference equations (with S. Garoufalidis) Contemporary Mathematics 410 (2006) 83-114
  • Riemann-Hilbert problems for multiple orthogonal polynomials (with W. Van Assche and A.B.J. Kuijlaars) NATO ASI proceedings Special Functions 2000: Current Perspectives and Future Directions, Tempe, Arizona, 2000
  • Polynomial Orthogonal with Respect to Singular Continuous Measures Orthogonal Polynomials and Their Applications, Springer Lecture Notes Vol. 132, 9, 32-45
  • Iterating Random Maps and Applications, Number Theory and Physics Springer Proceedings in Physics, 47, 209-215
  • An Application of Coxeter Groups to the Construction of Wavelet Bases in R^n (with D. Hardin and P. Massopust), Lecture Notes in Pure and Applied Math. 157 (1993) 157-196
  • Polynomials Orthogonal on the Unit Circle with Random Reflection Coefficients, US-USSR Conference on Approximation Theory, St. Petersburg, Russia, May 1991, Lecture Notes in Math. vol. 1550 Springer-Verlag