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arXiv · 2312.09724

Embeddings of block-radial functions -- approximation properties and nuclearity

Alicja Dota·Leszek Skrzypczak
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Abstract

Let $ R_\gamma B^{s}_{p,q}(\mathbb{R}d)$ be a subspace of the Besov space $B^{s}_{p,q}(\mathbb{R}^d)$ that consists of block-radial (multi-radial) functions. We study an asymptotic behaviour of approximation numbers of compact embeddings $id: R_\gamma B^{s_1}_{p_1,q_1}(\mathbb{R}^d) \rightarrow R_\gamma B^{s_2}_{p_2,q_2}(\mathbb{R}^d)$. Moreover we find the sufficient and necessary condition for nuclearity of the above embeddings. Analogous results are proved for fractional Sobolev spaces $R_\gamma H^s_p(\mathbb{R}^d)$.

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Alicja Dota, Leszek Skrzypczak. 2023-12-15. Embeddings of block-radial functions -- approximation properties and nuclearity. https://arxiv.org/abs/2312.09724

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