My research interests include wavelets, frames, and iterated function systems. A frame can be thought of as a generalization of an orthonormal basis for a Hilbert space. I recently co-authored an undergraduate-level introduction to frames, published by the American Mathematical Society. I am currently looking at harmonic properties of the equilibrium measures which arise from iterated function systems.
Publications
Orthogonal Exponentials for Bernoulli Iterated Function Systems, with P. Jorgensen and K. Shuman, accepted for publication in Proceedings for Current Trends in Harmonic Analysis and Its
Applications: Wavelets and Frames Workshop in Honor of Larry Baggett, Birkhauser. arXiv Listing: math.OA/0703385.
Frames for Undergraduates, with D. Han, D. Larson, and E. Weber. Student Mathematical Library, vol. 40. American Mathematical Society, Providence, RI, 2007.
Affine Systems: Asymptotics at Infinity for Fractal Measures , with P. Jorgensen and K. Shuman. Acta Applicandae Mathematica, vol. 98 (2007), no. 3, 181--222.
arXiv Listing: math-DS/0707.1263.
Harmonic Analysis of Iterated Function Systems with Overlap, with P. Jorgensen and K. Shuman. Journal of Mathematical Physics, vol. 48 (2007), no. 8, 083511, 35 pp.
arXiv Listing: math-ph/0701066.
Convolutional Frames and the Frame Potential , with M. Fickus, B. Johnson, and K.
Okoudjou, Appl. Comput. Harmon. Anal., vol. 19 (1),2005, 77-91.
Local Solvability of Laplacian Difference Operators Arising from
the Discrete Heisenberg Group, Canadian J. Math. vol.57 (3), 2005, 598-615.
Rank-One Decomposition of Operators and Construction of Frames, with D. Larson,
"Wavelets, Frames, and Operator Theory", Contemp. Math., vol. 345, Amer. Math. Soc., Providence, RI,
2004, 203-214.
Ellipsoidal Tight Frames and Projection Decomposition of Operators, with K. Dykema,
D. Freeman, D. Larson, M. Ordower, and E. Weber, Illinois J. Math, Vol. 48, Number 2, Summer 2004, 477 - 489.
Work in Progress
Non-Integer Translation Invariant Systems, with A. Aldroubi, C. Cabrelli, C. Heil, and U. Molter, in progress.
Iterated function systems, moments, and transformations of infinite matrices
, with P. Jorgensen and K. Shuman, in progress.
Upcoming Conferences
February 21-22, 2008 February Fourier Talks, Norbert Wiener Center for Harmonic Analysis and Applications, College Park, MD.