Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas
The work advances theoretical understanding of Hardy spaces and cubature error estimates in a specific domain relevant to conformal quantum field theory, but is incremental in nature.
The paper introduces a new concept of Hardy spaces on a multidimensional complexified annular domain related to the Klein-Dirac quadric, and provides error estimates for polyharmonic Gauß-Jacobi cubature formulas for functions in these spaces.
The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the annulus of the Klein-Dirac quadric important in Conformal Quantum Field Theory. Secondly, for functions in these Hardy spaces, we provide error estimate for the polyharmonic Gauß-Jacobi cubature formulas, which have been introduced in previous papers.