Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas
Ognyan Kounchev, Hermann Render
TL;DR
This paper introduces Hardy spaces on a complexified annulus related to quantum field theory and provides error estimates for specific cubature formulas used in multidimensional integration.
Contribution
It defines new Hardy spaces on a complexified annulus and derives error bounds for polyharmonic Gauß-Jacobi cubature formulas.
Findings
Defined Hardy spaces on complexified annuli related to Klein-Dirac quadric
Provided error estimates for polyharmonic Gauß-Jacobi cubature formulas
Linked mathematical theory to applications in Conformal Quantum Field Theory
Abstract
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 Gau\ss -Jacobi cubature formulas, which have been introduced in previous papers.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Advanced Mathematical Physics Problems