S EMINARIO DE A N ALISIS Y ´ A PLICACIONES
Viernes, 3 de octubre de 2014
11:30 h.,M ´odulo 17 (antiguo C-XV) - Aula 520(Depto. Matem ´aticas UAM)
Joaquim Ortega Cerd ` a
Universidad de Barcelona / Universitat de Barcelona
Marcinkiewicz-Zygmund inequalities in real algebraic varieties
Resumen:
I will present a joint work with Robert Berman where we consider the pro- blem sampling multivariate real polynomials of large degree in a general fra- mework where the polynomials are defined on an affine real algebraic variety equipped with a weighted measure.
It is shown that a necessary condition for sampling, in the general setting, is that the asymptotic density of sampling points is greater then the density of the corresponding weighted equilibrium measure, as defined in pluripotential theory.
This result thus generalizes the well-known Landau type results for sampling on the torus, where the corresponding critical density corresponds to the Nyq- vist rate, as well as the classical result saying that the zeroes of orthogonal poly- nomials become equidistributed with respect to the logarithmic equilibrium measure, as the degree tends to infinity.
ICMAT CSIC-UAM-UC3M-UCM
Departamento de Matem ´aticas. U.A.M.
