"Affine density and von Neumann dimension"Speckbacher, MichaelIn this talk, we will show how a new method to compute the von Neumann dimension of a factor can be used to provide a solution to an old problem about basis properties of affine coherent states (also known as analytic wavelets) labelled by Fuchsian groups. This problem can be traced back to the work of Perelomov in the early 70's. The solution contains the description of frames and Riesz sequences in certain wavelet phase-spaces in terms of a 'Nyquist rate', as typical of such problems for signal representations. Choosing the reproducing kernel as the vector to which the action of the Fuchsian group is applied, one can derive a description of wavelet frames and Riesz sequences. The value of the 'Nyquist rate' coincides with a conjecture of Kristian Seip in 1989. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Speckbacher_2021-07_extended-abstract-speckbacher.pdf |
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