The discussion was focused on some of the broader areas addressed in the talks and the following areas of current and future work were discussed. Contributors are identified in parentheses.

Finite Frame Theory:

• The Paulsen Problem: If a frame is close to being unit-norm and close to being tight, is it close to being a unit-norm, tight frame? (Matthew Fickus) Are perturbations of equal-norm tight frames close to other equal-norm tight frames? (Pete Casazza)


• Construction of equi-angular (real or complex) tight frames. Examples are known for certain dimensions, but there is a significant amount unknown in this area. (Pete Casazza, Matthew Fickus, and Ilya Krishtal)


• Classification of Parseval frames: When is it possible to partition equal-norm tight frames into pieces that possess a given useful property? (Pete Casazza)


• Measuring redundancy of frames. (Pete Casazza)


• Development of algorithmic constructions of Parseval frames. (Pete Casazza)

• Can one describe useful weighted fusion frames that generate a given frame? (Ilya Krishtal)


• Related to work of Donoho regarding the preservation of the variance of noise under certain transformations. Can [tight]-frames be defined so that the frame operator nearly preserves the variance of noise? More focus should be placed on statistics in the context of frames. (Charles Chui) There is a related paper by M. Elad in the IEEE Transactions on Information Theory discussing thresholding with frames. (Minh Do)


• Continuation of extension results for frames (e.g., Parseval frames are projections of orthonormal bases). When do such superframes preserve the [group] structure of the original frame? (Azita Mayeli)

• Let $P$ localize to $\Sigma$ in frequency and $Q$ localize to an interval of length $T$ in time. If $\Sigma$ = \argmax_{\vert \Sigma\vert = 1} \Vert P_{\Sigma} Q_{T} \Vert then $\Sigma$ must be an interval provided that $T<0.8$. Is this true for all $T$? What is the optimal shape of such sets in higher dimensions? (Joe Lakey)

• On the existence of compactly supported composite wavelet functions: What middle ground exists between the results of Houska and Lim? (Edward Wilson)


• Is there a version of Cohen's Criterion for multiple scaling functions? (Ilya Krishtal)