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Analysis Seminar with Olof Rubin (Lund University)

Tid: 2023-03-22 14:15 till 15:15 Seminarium

Chebyshev Polynomials on polynomial preimages

Speaker: Olof Rubin (Lund University)

Abstract: In the talk I will discuss Chebyshev polynomials in the complex plane. Given an infinite compact set E ⊆ C the Chebyshev polynomial of degree n associated with E is the unique monic polynomial of degree n which minimises the supremum norm on E.

I will mainly discuss the asymptotical behaviour of Chebyshev polynomials on certain sets which are given as polynomial preimages. I shall also show that a general conjecture for the relation between orthogonal polynomials
and Chebyshev polynomials holds for this class of domains. Much of our work was preceded by a study using numerical algorithms, in particular a complex generalisation of the Remez algorithm. If time permits I will present further conjectures on the asymptotical behaviour of Chebyshev polynomials that we have gotten from the use of this algorithm.

The talk is based on joint work with Jacob Stordal Christiansen at Lund University and Benjamin Eichinger at TU Wien.

Om händelsen
Tid: 2023-03-22 14:15 till 15:15


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Sidansvarig: webbansvarig@math.lu.se | 2017-05-23