Publications
- 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
-
Varying weights for
orthogonal polynomials with monotonically varying recurrence
coefficients (with Walter Van Assche and Alexander Aptekarev)
JAT 150 (2007) 214-238
-
Two
variable orthogonal polynomials on the bicircle and structured
matrices (with Hugo Woerdeman) SIAM J Matrix Anal. Appl. 29
(2007) 796-825
-
Two Variable polynomials Intersecting zeros and stability
(with H Woerdeman) IEEE Trans Circuits and Systems 53 (2006)
1130-1139
-
Two
variable orthogonal polynomials and structured matrices (with
A. Delgado, P. Iliev, and F. Marcellan) SIAM J. Matrix Anal. 28
(2006) 118-114
- Factorization
of multivariate positive Laurent polynomials (with M-J Lai) JAT
139 (2006) 327-345
- On
extensions of a Theorem of Baxter (with A.
Martinez-Finkelstein) JAT 139 (2006) 214-222
- 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
- Asymptotics
for Sobolev Orthogonal Polynomials for Exponential Weights(with
D. Lubinsky and P. Marcellan) Const. Appr. 22 (2005) 309-346
- Algebro-Geometric
Solutions of the Baxter-Szego Difference Equation (with F.
Gesztesy and H. Holden) CMP 258 (2005) 149-177
- Positive
extensions and Fejer-Riesz factorization for two-variable
trigonometric polynomials (with H. Woerdeman) Annals of Math.
160 (2004) 839-906
- 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
- A
Numerical Algorithm for the 2D Autoregressive Filter Problem
(with H. Woerdeman and G. Castro) IEEE Transactions in Signal Proc.
83 (2003) 1299-1308
- Certain
Two Dimensional Integrals that Appear in Conformal Field Theory
(with H. Navelet) J. Math Physics, 44 (2003) 2293-2319
- 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
- Squeezable
Orthogonal Bases: Accuracy and Smoothness
(with
G. Donovan and D. Hardin) SIAM J. Numer. Anal. 40 (2002) 1077-1096
- Compactly
Supported, Piecewise Affine Scaling Functions on Triangulations
(with G.Donovan and D. Hardin) Const. Approx. 16 (2000) 201-219
- Orthogonal
Polynomials and the Construction of Piecewise Polynomial Smooth
Wavelets (with G. Donovan and D. Hardin) SIAM J. Math. Anal. 30
(1998) 1029-1056
- An
Inverse Problem Associated with Polynomials Orthogonal on the Unit
Circle (with R. Johnson) Commun. Math Phys. 193 (1998) 125-150
-
The
Inverse Fractal Problem for Polyhulled Disjoint Attractors
(with A. Delui and R. Shonkwiler) Phil. Trans. R. Soc. Lond A 355
(1997) 1017-1062
- Design
of Prefilters for Discrete Multiwavelet Transforms (with X.
Xia, D. Hardin and B. Suter) IEEE Trans. Signal Proc. 44 (1996) 25-35
-
Construction
of orthogonal wavelets using fractal interpolation functions
(with G. Donovan, D. Hardin and P. Massopust) SIAM J. Math. Anal. 27
(1996) 1158-1192
- Interwining
multiresolution analysis and the construction of piecewise polynomial
wavelets (with G. Donovan, and D. Hardin) SIAM J. Math. Anal.
27 (1996) 1791-1815
-
Rotation
Number Associated with Polynomials Orthogonal on the Unit Circle
(with R. Johnson) JDE 132 (1996) 140-178
-
Fractal
functions and wavelet expansions based on several scaling functions
(with D. Hardin and P. Massopust) J. Approx. Theory 78 (1994) 373-401
-
Scattering
Theory, Orthogonal Polynomials and Q-series, SIAM J. Math.
Anal. 25 (1994) 392-419
-
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
-
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
-
Fractal
Interpolation Surfaces with an Application to a Two-Dimensional
Multiresolution Analysis (with D. Hardin), J. Math Anal. and
App. 176 (1993) 561-586
-
Singularity
Spectrum for Recurrent IFS Attractors (with J. F. King)
Nonlinearity 6 (1992) 337-348
-
WKB
(Louisville-Green) Analysis of Second Order Difference Equations and
Applications (with D. Smith) J. Approx. Theory 69 (1992)
269-301
-
Approximating
the weight function for orthogonal polynomials on several intervals
(with W. Van Assche) J. Approx. Theory 65 (1991) 341-371
- Dimensions
associated with recurrent self-similar sets (with A. Deliu, D.
Hardin and R. Shonkwiler), Math. Proc. Camb. Phil. Soc. 110 (1991)
327-336.
- 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
- Relative
Asymptotics for Orthogonal Polynomials with Unbounded Recurrence
Coefficients (with
W. Van Assche) J. Approx. Theory 62 (1990) 47-69
- Capacities
of Measures Associated with Iterated Function Systems (with D.
Hardin) Const. Approx. 5 (1989) 89-98
- Asymptotics
for Orthogonal Polynomials with Unbounded Recurrence Coefficients
(with W. Van Assche), Rocky Mountain J. Math. (19) (1989) 39-49
-
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
-
Orthogonal
Polynomials on Several Intervals via a Polynomial Mapping (with
W. Van Assche) Trans. Amer. Soc. 308 (1988) 559-581
-
Asymptotics
for Orthogonal Polynomials On and Off the Essential Spectrum
(with W. Van Assche) J. Approx. Theory. 55 (1988) 220-231
-
On
the Asymptotic Distribution of Eigenvalues of Banded Matrices
(with E. M. Harrell II and W. Van Assche) Const. Approx. 4 (1988)
403-417
-
Function
Weighed Measures and Orthogonal Polynomials on Julia Sets (with
D. Bessis and P. Moussa) Const. Approx. 4 (1988) 157-173
-
On
the Spectra of Infinite Dimensional Jacobi Matrices, J. Approx.
Theory 53 (1988) 251-265
-
Orthogonal
Polynomials with Asymptotically Periodic Recurrence Coefficients
(with W. van Assche) J. Approx. Theory 46 (1986) 251-283
-
Almost
Periodic Operators Associated with Julia Sets (with M. F.
Barnsley and A. N. Harrington) Comm. Math. Phys. 99 (1985) 303-317
-
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
-
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
-
Mellin
Transforms Associated with Julia Sets and Physical Applications
(with D. Bessis and P. Moussa) J. Stat. Phys. 34 (1984) 75-110
-
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
-
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
-
Complex
Spectral Dimensionality on Fractal Structures (with D. Bessis
and P. Moussa) J. Physique.-Lett. 44 (1983) 977-982
-
Some
Tree-like Julia Sets and Pade Approximants (with M. F. Barnsley
and A. N. Harrington) Lett. Math. Phys. 7 (1983) 279-286
-
Infinite
Dimensional Jacobi Matrices Associated with Julia Sets (with M.
F. Barnsley and A. N. Harrington) Proc. Am. Math. Soc. 88 (1983)
625-630
-
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
-
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
-
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
-
Scattering
Theory and Matrix Orthogonal Polynomials on the Real Line,
Circuits Systems Signal Process I (1982) 471-495
-
An
Upper Bound on the Number of Eigenvalues of an Infinite Dimensional
Jacobi Matrix, J. Math. Phys. 23 (1982) 917-921
-
Matrix
Orthogonal Polynomials on the Unit Circle, J. Math. Phys. 22
(1981) 1359-1365
-
A
Relation Between the Coefficients in the Recurrence Formula and the
Spectral Function for Orthogonal Polynomials, Trans. Amer. Math.
Soc. 260 (1980) 65-82
-
Scattering
Theory and Polynomials Orthogonal on the Real Line (with K. M.
Case) Trans. Amer. Math. Soc. 258 (1980) 467-494
-
Szego's
Theorem on Hankel Determinants, J. Math. Phys. 20 (1979) 484-491
-
Scattering
Theory and Polynomials Orthogonal on the Unit Circle (with K.
M. Case) J. Math. Phys. 20 (1979) 299-320
-
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