Hardy spaces on the Klein-Dirac quadric and multidimensional annulus: applications to Interpolation, Moment problems, and Cubature
We present a new construction of Hardy spaces on the Klein-Dirac
quadric; we show that the quadric is obtained as a complexification of the
unit ball in R^n. We introduce also Hardy spaces on complexified
We show some natural properties of these Hardy spaces, in particular,
Cauchy type formula, and Brothers Riesz type theorem.
We prove applications to the multidimensional Moment problem,
multidimensional Interpolation theory, and Cubature formulas.