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Oberwolfach Workshop 1309: Structured function systems and applications

February 24 - March 3, 2013

Organizers

• Maria Charina, Technische Universität Dortmund, Germany
• Jean-Bernard Lasserre, LAAS-CNRS, France
• Mihai Putinar, University of California at Santa Barbara, USA
• Joachim Stöckler, Technische Universität Dortmund, Germany

Topics

• Multivariate Wavelet and Gabor Frames: families of functions generated by action of a discrete group (e.g. subgroups of the Heisenberg group or the affine group) on a single function
• Multivariate Moment Problems
• Nonconvex Polynomial Optimization and Positivity Certificates
• Function theory of several complex variables

Goal of the workshop

inspire fruitful interdisciplinary cooperation and advances in control theory, function theory of several complex variables, moment problems, real algebraic geometry and semi-definite programming that promise to have impact on theory and computational aspects of structured function systems.

Outline

five thematic days devoted to recent advances in above mentioned topics.

Description

The goal of this workshop is to explore and deepen newly discovered links between Gabor and wavelet analysis on the one side and real algebraic geometry, complex analysis and optimization on the other. Among concrete and motivating applications is the construction of systems (not necessarily frames or bases) of special functions with the aid of: positivity certificates derived with real algebra tools, recent advances in multivariate moment problems and the spectacular progress made during the last decade in non-convex, polynomial optimization. Some of the guiding and long standing open problems in structured function systems to be addressed during the workshop are: multivariate wavelet frame constructions via sums of squares representations of non-negative Laurent polynomials; computerized, self-contained interface for frame constructions via semi-definite programming; an upper bound for the number of frame generators v.s an estimate of the Pythagoras number of the ring of multivariate Laurent polynomials; Gabor analysis/time-frequency analysis via sampling and bounded interpolation problems in complex analysis of one and several complex variables.