- Series
- Analysis Seminar
- Time
- Wednesday, November 13, 2013 - 3:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Shahaf Nitzan – Kent State
- Organizer
- Brett Wick
This talk discusses exponential frames and Riesz sequences in L^2 over a set
of finite measure. (Roughly speaking, Frames and Riesz sequences are over
complete bases and under complete bases, respectively). Intuitively, one
would assume that the frequencies of an exponential frame can not be too
sparse, while those of an exponential Riesz sequence can not be too dense.
This intuition was confirmed in a very general theorem of Landau, which
holds for all bounded sets of positive measure.
Landau's proof involved a deep study of the eigenvalues of compositions of
certain projection operators. Over the years Landaus technique, as well as
some relaxed version of it, were used in many different setting to obtain
results of a similar nature.
Recently , joint with A. Olevskii, we found a surprisingly simple approach
to Landau's density theorems, which provides stronger versions of these results. In particular,
the theorem for Riesz sequences was extended to unbounded sets (for frames,
such an extension is trivial).
In this talk we will discuss Landau's results and our approach for studying
questions of this type.