Sets of $p$-restriction and $p$-spectral synthesis

Michael J. Puls

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arXiv · 1904.02282

Sets of $p$-restriction and $p$-spectral synthesis

Michael J. Puls

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Abstract

In this paper we investigate the restriction problem. More precisely, we give sufficient conditions for the failure of a set $E$ in $\mathbb{R}^n$ to have the $p$-restriction property. We also extend the concept of spectral synthesis to $L^p(\mathbb{R}^n)$ for sets of $p$-restriction when $p > 1$. We use our results to show that there are $p$-values for which the unit sphere is a set of $p$-spectral synthesis in $\mathbb{R}^n$ when $n \geq 3$.

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BibTeX RIS

Michael J. Puls. 2019-04-04. Sets of $p$-restriction and $p$-spectral synthesis. https://arxiv.org/abs/1904.02282

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