Publications
Support from the NSF, and the
University of Illinois Research Board, the New Zealand Institute for
Mathematics and its Applications, and the Visiting Erskine Fellowship at
the University of Canterbury, is gratefully acknowledged.
Here is my publication list, followed by summaries of the papers. You might
also enjoy this discussion of
journal impact
factors.
Please e-mail me
if you have trouble downloading the files you want.
- Gabor dual spline windows
26 pages. Submitted, 2008.
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preprint.
- A note on constructing affine systems for L2
(With H.-Q. Bui and N. Kaiblinger.)
Applied and Computational Harmonic Analysis, 7 pages, appeared online
2008.
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reprint.
- A computable Fourier condition
generating alias-free sampling lattices
(With Y. M. Lu and M. N. Do.)
IEEE Transactions on Signal Processing, 30 pages, to appear.
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preprint.
- Moment inequalities for equilibrium measures in the plane
(With A. Baernstein II and I. E. Pritsker.)
Pure and Applied Mathematics Quarterly, 28 pages, to appear.
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preprint.
- Affine synthesis onto Lp when 0 < p <= 1
Journal of Fourier Analysis and Applications, 14:235-266, 2008.
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reprint.
- Affine synthesis onto Lebesgue and Hardy spaces
(With H.-Q. Bui.)
Indiana University Mathematics Journal, 26 pages, to appear.
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preprint.
Paper 28 is a revised version of the following preprint, which treats
Sobolev spaces too:
Affine synthesis and coefficient norms for Lebesgue, Hardy and
Sobolev spaces
(With H.-Q. Bui.)
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preprint.
- Sobolev spaces and approximation by affine spanning
systems
(With H.-Q. Bui.)
Mathematische Annalen, 341:347-389, 2008.
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reprint.
- Approximation and spanning in the Hardy space, by affine
systems
(With H.-Q. Bui.)
Constructive Approximation, 28:149-172, 2008.
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reprint.
- On convex surfaces with minimal moment of inertia
(With P. Freitas and G. F. Liddell.)
Journal of Mathematical Physics, 48, 122902, 2007.
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reprint.
- On affine frames with transcendental dilations
Proceedings of the American
Mathematical Society, 135:211-216, 2007.
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reprint.
- Affine systems that span Lebesgue spaces
(With H.-Q. Bui.)
Journal of Fourier Analysis and Applications, 11:533-556, 2005.
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reprint.
Papers 23 and 27 are based on the following research report:
Spanning and sampling in Lebesgue and Sobolev spaces
(With H.-Q. Bui.)
University of Canterbury Research Report UCDMS2004/8, 64 pages.
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preprint.
- New dissipated energies for the thin fluid film equation
Communications on Pure
and Applied Analysis, 4:613-634, 2005.
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reprint.
- Another way to say subsolution: the maximum principle and
sums of Green functions
(With N. A. Watson.)
Mathematica Scandinavica,
97:127-153, 2005.
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reprint.
- Potential theory of the farthest-point distance function
(With Igor E. Pritsker.)
Canadian Mathematical Bulletin, 46:373-387, 2003.
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reprint.
- Heteroclinic orbits, mobility parameters and stability for
thin film type equations
(With Mary C. Pugh.)
Electronic Journal of Differential Equations, 2002: No. 95, 1-29.
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- Energy levels of steady states for thin film type equations
(With Mary C. Pugh.)
Journal of Differential Equations, 182:377-415, 2002.
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reprint.
- A characterization of the higher dimensional
groups associated with continuous wavelets
(With Nik Weaver, Guido Weiss and Edward Wilson.)
Journal of Geometric Analysis 12:89-102, 2002.
No reprints available.
- Translational averaging for completeness, characterization and
oversampling of wavelets
Collectanea Mathematica, 53:211-249, 2002.
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reprint.
- Completeness of orthonormal wavelet systems, for arbitrary
real dilations
Applied and Computational Harmonic Analysis, 11:455-473, 2001.
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reprint.
- Linear stability of steady states for thin film and
Cahn-Hilliard type equations
(With Mary C. Pugh.)
Archive for Rational Mechanics and Analysis, 154:3-51, 2000.
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reprint.
- Properties of steady states for thin film equations
(With Mary C. Pugh.)
European Journal of Applied Mathematics, 11(3):293-351, 2000.
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reprint.
- Binary forms, equiangular polygons and harmonic measure
(With Michael A. Bean.)
Rocky Mountain Journal of Mathematics, 30:15-62, 2000.
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reprint.
- Eigenvalues of strings and cylinders with variable mass
density
Communications in Analysis and Geometry, 8:393-443, 2000.
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reprint.
- Eigenvalues of the Laplacian on inhomogeneous membranes
American Journal of Mathematics, 120:305-344, 1998.
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reprint.
- Eigenvalues of Laplacians with mixed boundary conditions,
under conformal mapping
Illinois Journal of Mathematics, 42:19-39, 1998.
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reprint.
- Extremals for eigenvalues of Laplacians under conformal
mapping
(With Carlo Morpurgo.)
Journal of Functional Analysis, 155:64-108, 1998.
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reprint.
- Planar harmonic maps with inner and Blaschke dilatations
Journal of the London Mathematical Society, 56:37-48, 1997.
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reprint.
- Inequalities for the first eigenvalues of the clamped plate
and buckling problems
(With Mark S. Ashbaugh and Rafael D. Benguria.)
International Series of Numerical Mathematics, Volume 123
(Proceedings of the Oberwolfach Conference "General Inequalities 7"),
pp. 95-110, 1997.
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reprint.
- Fundamental tones and buckling loads of clamped plates
(With Mark S. Ashbaugh.)
Annali della Scuola Normale Superiore di Pisa, 23:383-402, 1996.
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reprint.
- The argument principle for harmonic functions
(With Peter L. Duren and Walter Hengartner.)
American Mathematical Monthly, 103:411-415, 1996
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reprint.
- Injectivity can fail for higher-dimensional harmonic
extensions
Complex Variables, 28:357-369, 1996.
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reprint.
- Conformal mapping of long quadrilaterals and thick doubly
connected
domains
Constructive Approximation, 10:523-554, 1994.
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reprint.
- Extremal problems involving logarithmic and Green capacity
Duke Mathematical Journal, 70:445-480, 1993.
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reprint.