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Colloquia Patavina: The moment problem for positive rational measures: convexity in the spirit of Krein

ARGOMENTI: Seminari

Martedi' 13 Ottobre 2009 alle ore 16:00 in aula 1A/150 della Torre Archimede il Prof. Anders Lindquist (Royal Institute of Technology) terra' una conferenza della serie Colloquia Patavina.

La Commissione Colloquia
M.A. Garuti, M. Pavon, M. Pitteri, F. Rossi

-Titolo
The moment problem for positive rational measures: convexity in the
spirit of Krein

-Conferenziere
Anders Lindquist (Royal Institute of Technology)

-Riassunto
The moment problem as formulated by Krein and Nudel'man is a beautiful generalization of several important classical moment problems, including the power moment problem, the trigonometric moment problem and the moment problem arising in Nevanlinna-Pick interpolation. However, the importance of rational functions in systems and control and other engineering applications imposes certain complexity constraints. In this talk we present a new formulation of the moment problem which respects these constraints. While this version of the problem is decidedly nonlinear, the basic tools still rely on convexity. We give a complete parameterization of all solutions. This can be seen as a global analysis approach, where one studies an entire class of solutions as a whole. We then show that each solution in this class can be obtained by minimizing a strictly convex nonlinear functional. Thus the methodology employed is a combination of nonlinear analysis, geometry and optimization. Finally, we apply these results to interpolation problems of the Caratheodory and of the Nevanlinna-Pick type, arising in signal processing and control theory, where we consider smooth bijective transformations from spaces of tuning parameters to entire classes of solutions.

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