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Wednesday, April 27 (4:00pm in Kerchof 317)
Yuan Xu (University of Oregon) Reconstruction of Images from the Radon Projections Let the image be represented by a function f. A Radon projection is a line integral of f. The main problem for image reconstruction from the Radon projections is to recover f from its Radon projections. This question is completely solved if the continuous data is known. In practice, however, only a finite number of projections can be measured. Hence, the essential problem is to find a good approximation to f using a finite number of the Radon projections. We discuss a new approach based on orthogonal polynomials of several variables. Refreshments served at 3:30 in Kerchof Hall Common Room (314)
Thursday, April 28 (4:00pm in Kerchof 317)
Yuri Berest (Cornell University) The Shift Principle for Real and Complex Reflection Groups One of the first striking applications of Dunkl operators was Heckman's elementary construction of multivariable shift operators for finite Coxeter groups. The existence of such operators has many important implications for analysis, algebra and geometry related to classical root systems. More recently, Dunkl and Opdam introduced a version of Dunkl operators for an arbitrary complex reflection group and asked whether Heckman's construction could be extended to this more general setting. In this talk, which will be partly an introductory survey accessible to graduate students, I will answer this question in affirmative and discuss some implications. Refreshments served at 3:30 in Kerchof Hall Common Room (314)
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