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arXiv · 2307.02220

Spherical Basis Functions in Hardy Spaces with Localization Constraints

Christian Gerhards·Xinpeng Huang
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Abstract

Subspaces obtained by the orthogonal projection of locally supported square-integrable vector fields onto the Hardy spaces $H_+(\mathbb{S})$ and $H_-(\mathbb{S})$, respectively, play a role in various inverse potential field problems since they characterize the uniquely recoverable components of the underlying sources. Here, we consider approximation in these subspaces by a particular set of spherical basis functions. Error bounds are provided along with further considerations on norm-minimizing vector fields that satisfy the underlying localization constraint. The new aspect here is that the used spherical basis functions are themselves members of the subspaces under consideration.

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Christian Gerhards, Xinpeng Huang. 2023-07-05. Spherical Basis Functions in Hardy Spaces with Localization Constraints. https://arxiv.org/abs/2307.02220

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