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Polyharmonic Hardy spaces on the complexified annulus and error estimates of cubature formulas. (English) Zbl 1253.41029
Summary: 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.

MSC:
41A55 Approximate quadratures
65D30 Numerical integration
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
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