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Simultaneous approximation by polynomials

Presented by: 
Yuan Xu University of Oregon, University of Oregon
Monday 29th April 2019 - 14:00 to 16:00
INI Seminar Room 2
Least square polynomials in an $L^2$ space are partial sums of the Fourier orthogonal expansions. If we were to approximate functions and their derivatives simultaneously on a domain in $R^d$ (as desired in spectral method), we would need to consider orthogonal expansions in a Sobolev space, for which the orthogonality is defined with respect to an inner product that contains derivatives. Since multiplication operators are no longer self-adjoint under such an inner product, the orthogonality is hard to understand and analyze. In the talk we will explain what is known.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons