Constrained L2-approximation by polynomials on subsets of the circle

Laurent Baratchart (1) , Juliette Leblond (1) , Fabien Seyfert (1)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing

We study best approximation to a given function, in the least square sense on a subset of the unit circle, by polynomials of given degree which are pointwise bounded on the complementary subset. We show that the solution to this problem, as the degree goes large, converges to the solution of a bounded extremal problem for analytic functions which is instrumental in system identification. We provide a numerical example on real data from a hyperfrequency filter.

Domaines: Analyse fonctionnelle [math.FA]

Laurent Baratchart, Juliette Leblond, Fabien Seyfert. Constrained L2-approximation by polynomials on subsets of the circle. Mashreghi, Javad; Manolaki, Myrto; Gauthier, Paul M. New Trends in Approximation Theory. In Memory of André Boivin, 81, Springer, pp.151-171, 2018, Fields Institute Communications, 978-1-4939-7543-3. ⟨10.1007/978-1-4939-7543-3_8⟩. ⟨hal-01671183v2⟩