Title:
Pseudodifferential operators, Banach algebras, and mobile communications
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Recent theoretical advances at the interface of pseudodifferential operators, 
time-frequency analysis and Banach algebras have unearthed a
surprising link to a rather applied area, namely communications engineering.
Unlike classical telecommunication, whose fundamental principles can
be described via commutative harmonic analysis, the analysis and
design of modern mobile communication systems requires methods 
from noncommmutative harmonic analysis.
We will see that the modeling of the mobile radio channel leads to
interesting problems in pseudodifferential operator theory. 
Their treatments lies outside the standard theory of PDEs, and requires 
tools from time-frequency analysis and Banach algebra theory.
For instance, I will show that Weyl-Heisenberg systems provide an optimally 
sparse representation of these non-standard pseudodifferential operators. 
These results can even be generalized
to the abstract setting of locally compact abelian groups.
Finally, if time permits, I will show how the theoretical framework presented 
in this talk has already found its way into the design of real-world
communication systems.