Analysis seminar: Sharp Hankel operators and de Saint-Venant’s inequality

2 November 2015, 4.00 PM - 2 November 2015, 5.00 PM

Maria Carmen Reguera, University of Birmingham

Howard House, 4th floor seminar room

Abstract:

de Saint-Venant's inequality is an isoperimetric inequality that relates the torsional rigidity of a cylindrical object with the area of its cross-section.  In this talk, we will present a new proof of this classical inequality using operator theory. In particular, we look for sharp estimates for Hankel operators with anti-analytic symbols in the Bergman space.  The estimate we obtain improves a classical inequality in operator theory for commutators of Toeplitz operators known as Putnam’s inequality.  This improvement answers a recent conjecture by Bell, Ferguson and Lundberg.  The operator theory approach to isoperimetric inequalities was first used by Khavinson in 1985, who obtained the classical isoperimetric inequality that relates area and perimeter of the region using Putnam’s inequality for the commutator of Toeplitz operators in the Hardy space.  This is joint work with J-F Olsen.

Contact information

Organisers: Michiel van den BergJohn Mackay

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