Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas
arXiv:1205.64143 citationsh-index: 13
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This work provides a theoretical foundation for polyharmonic interpolation and cubature on a specific geometric structure, but its practical impact is unclear.
The paper introduces a new concept of Hardy type spaces on the Klein-Dirac quadric and studies their properties, applying them to polyharmonic interpolation and cubature formulas. No concrete numerical results are provided.
In the present paper we introduce a new concept of Hardy type space naturally defined on the Klein-Dirac quadric. We study different properties of the functions belonging to these spaces, in particular boundary value problems. We apply these new spaces to polyharmonic interpolation and to interpolatory cubature formulas.