# on Herz's extension theorem

Document Type: Original Article

Author

Ecole Polytechnique de Lausanne, Switzerland

Abstract

{Large Abstract. We present a self-contained proof of the following famous extension theorem due to Carl Herz. A closed subgroup $H$ of a locally compact group $G$ is a set of $p$hskip1pt-synthesis in $G$ if and only for every hbox{$uin A_p(H)cap C_{00}(H)$} and for every $varepsilon >0$ there is hbox{$vin A_p(G)cap C_{00}(G),$} an extension of $u,$ such that|v|_{A_p(G)}

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### Histroty

• Receive Date: 10 September 2018
• Revise Date: 15 November 2018
• Accept Date: 16 November 2018