This seminar is organized each Spring by analysis aficionados at New Mexico State University and The University of New Mexico. The goal is to provide an opportunity for scientific exchange and cooperation among broadly defined analysts. The centerpiece of the seminar is a series of one-hour lectures given by a keynote speaker. There is time allocated for shorter contributed talks. If you would like to attend and/or give a talk, please contact one of the organizers by January 15, 2002. Doctoral students and recent PhDs are specially encouraged to apply.

The seminar is being sponsored by NSF. We will provide travel stipends for qualified graduate students. We intend to pay, at least partially, shared accommodations for all participants, and if there are funds left, for some travel expenses for those who have no other sources of fundind (priority given to speakers).

Organizers: Josefina Alvarez (jalvarez@math.nmsu.edu), Joseph Lakey (jlakey@ math.nmsu.edu), Cristina Pereyra (crisp@math.unm.edu).

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Titles:

Lecture 1. Wavelet theory and a fundamental application

Lecture 2. Multidimensional wavelet theory: multiresolution analysis (MRA) and non-MRA

Lecture 3. Fourier frames and weighted Fourier transform inequalities

Abstract for the series:

In the first lecture we present elementary wavelet theory, including an historical background and the role of the uncertainty principle. The fundamental ap
plication is also elementary to explain, and is motivated by classical problems in spectral estimation. Its origins are in the problem of epileptic seizure prediction.

The second lecture presents the theory of multidimensional wavelet theory, and provides basic constructions fo single dyadic orthonormal multidimensional wavelets. These constructions were unexpected in the mid-1990s and are intimately related with fractal sets and the notion of self-similarity.

The third lecture deals with the theory of Fourier frames, versus the wavelet frames of the first lecture. In the finite case, we study Platonic solids and in the infinite case we solve a data acquisition problem in MRI. We close by proving new Fourier transform norm inequalities, which, in turn, give rise to uncertainty principle inequalities of the type which arose in the first lecture.

The speaker's own results in these talks represent joint work with David Colella, Matthew Fickus, Hans Heinig, Goetz Pfander, Songkiat Sumetkijakan, and Hui-Chuan Wu.

For more information as it becomes available, go to Joseph Lakey's New Mexico Analysis Seminar information page.

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