On the growth of Lebesgue constants for convex polyhedra
The talk is devoted to the Lebesgue constants of polyhedral partial sums of the Fourier series.
New upper and lower estimates of the Lebesgue constant in the case of anisotropic dilations of
general convex polyhedra will be presented. The obtained estimates generalize and give sharper
versions of the corresponding results of E.S. Belinsky (1977), A.A.Yudin and V.A. Yudin (1985),
J.M. Ash and L. De Carli (2009), and J.M. Ash (2010).