The numerical range: a survey of classical results and some recent developments
Ilya M. Spitkovsky, College of William and Mary (USA) and New York University Abu Dhabi (United Arab Emirates) (cartel)
Viernes 13 de junio, ICMAT, Aula Naranja, 11:30
- Possible shapes of the numerical range in finite dimensional case (which is actually a harder question than its infinite dimensional version), including persistence of ellipticity in higher dimensions and flat portions phenomenon on the boundary;
- Continuity properties of the inverse generating function, that is, the (multivalued) inverse of the mapping \[ x\to (Ax,x)\]. The notions of strong and weak continuity will be introduced, and criteria for each of them to hold/fail established, both in terms of the geometry of the numerical range and analytic properties of the associated eigenfunctions.