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.

  1. Gabor dual spline windows
    26 pages. Submitted, 2008.
    Download preprint.

  2. 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.
    Download reprint.

  3. 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.
    Download preprint.

  4. 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.
    Download preprint.

  5. Affine synthesis onto Lp when 0 < p <= 1
    Journal of Fourier Analysis and Applications, 14:235-266, 2008.
    Download reprint.

  6. Affine synthesis onto Lebesgue and Hardy spaces
    (With H.-Q. Bui.)
    Indiana University Mathematics Journal, 26 pages, to appear.
    Download 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.) Download preprint.

  7. Sobolev spaces and approximation by affine spanning systems
    (With H.-Q. Bui.)
    Mathematische Annalen, 341:347-389, 2008.
    Download reprint.

  8. Approximation and spanning in the Hardy space, by affine systems
    (With H.-Q. Bui.)
    Constructive Approximation, 28:149-172, 2008.
    Download reprint.

  9. On convex surfaces with minimal moment of inertia
    (With P. Freitas and G. F. Liddell.)
    Journal of Mathematical Physics, 48, 122902, 2007.
    Download reprint.

  10. On affine frames with transcendental dilations
    Proceedings of the American Mathematical Society, 135:211-216, 2007.
    Download reprint.

  11. Affine systems that span Lebesgue spaces
    (With H.-Q. Bui.)
    Journal of Fourier Analysis and Applications, 11:533-556, 2005.
    Download 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.
    Download preprint.

  12. New dissipated energies for the thin fluid film equation
    Communications on Pure and Applied Analysis, 4:613-634, 2005.
    Download reprint.

  13. Another way to say subsolution: the maximum principle and sums of Green functions
    (With N. A. Watson.)
    Mathematica Scandinavica, 97:127-153, 2005.
    Download reprint.

  14. Potential theory of the farthest-point distance function
    (With Igor E. Pritsker.)
    Canadian Mathematical Bulletin, 46:373-387, 2003.
    Request reprint.

  15. 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.
    Download reprint.

  16. Energy levels of steady states for thin film type equations
    (With Mary C. Pugh.)
    Journal of Differential Equations, 182:377-415, 2002.
    Request reprint.

  17. 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.

  18. Translational averaging for completeness, characterization and oversampling of wavelets
    Collectanea Mathematica, 53:211-249, 2002.
    Request reprint.

  19. Completeness of orthonormal wavelet systems, for arbitrary real dilations
    Applied and Computational Harmonic Analysis, 11:455-473, 2001.
    Request reprint.

  20. 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.
    Request reprint.

  21. Properties of steady states for thin film equations
    (With Mary C. Pugh.)
    European Journal of Applied Mathematics, 11(3):293-351, 2000.
    Request reprint.

  22. Binary forms, equiangular polygons and harmonic measure
    (With Michael A. Bean.)
    Rocky Mountain Journal of Mathematics, 30:15-62, 2000.
    Request reprint.

  23. Eigenvalues of strings and cylinders with variable mass density
    Communications in Analysis and Geometry, 8:393-443, 2000.
    Request reprint.

  24. Eigenvalues of the Laplacian on inhomogeneous membranes
    American Journal of Mathematics, 120:305-344, 1998.
    Request reprint.

  25. Eigenvalues of Laplacians with mixed boundary conditions, under conformal mapping
    Illinois Journal of Mathematics, 42:19-39, 1998.
    Request reprint.

  26. Extremals for eigenvalues of Laplacians under conformal mapping
    (With Carlo Morpurgo.)
    Journal of Functional Analysis, 155:64-108, 1998.
    Request reprint.

  27. Planar harmonic maps with inner and Blaschke dilatations
    Journal of the London Mathematical Society, 56:37-48, 1997.
    Request reprint.

  28. 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.
    Request reprint.

  29. Fundamental tones and buckling loads of clamped plates
    (With Mark S. Ashbaugh.)
    Annali della Scuola Normale Superiore di Pisa, 23:383-402, 1996.
    Request reprint.

  30. The argument principle for harmonic functions
    (With Peter L. Duren and Walter Hengartner.)
    American Mathematical Monthly, 103:411-415, 1996
    Request reprint.

  31. Injectivity can fail for higher-dimensional harmonic extensions
    Complex Variables, 28:357-369, 1996.
    Request reprint.

  32. Conformal mapping of long quadrilaterals and thick doubly connected domains
    Constructive Approximation, 10:523-554, 1994.
    Request reprint.

  33. Extremal problems involving logarithmic and Green capacity
    Duke Mathematical Journal, 70:445-480, 1993.
    Request reprint.