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Simultaneous approximation by polynomials

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ASC - Approximation, sampling and compression in data science

Least square polynomials in an $L2$ space are partial sums of the Fourier orthogonal expansions. If we were to approximate functions and their derivatives simultaneously on a domain in $Rd$ (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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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