Advances in Operator Theory

On Herz's extension theorem

Antoine Derighetti

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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 $p$-synthesis in $G$ if and only if‎, ‎for every $u\in A_p(H)\cap C_{00}(H)$ and for every $\varepsilon > 0$‎, ‎there is $v\in A_p(G)\cap C_{00}(G)$, an extension of $u$, such that \[\|v\|_{A_p(G)} < \|u\|_{A_p(H)}+\varepsilon.\]

Article information

Source
Adv. Oper. Theory, Volume 4, Number 2 (2019), 529-538.

Dates
Received: 10 September 2018
Accepted: 16 November 2018
First available in Project Euclid: 1 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.aot/1543633242

Digital Object Identifier
doi:10.15352/aot.1809-1417

Mathematical Reviews number (MathSciNet)
MR3883151

Zentralblatt MATH identifier
1062.43005

Subjects
Primary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

Keywords
locally compact group‎ ‎ ‎set of spectral synthesis ‎ ‎‎‎extension property

Citation

Derighetti, Antoine. On Herz's extension theorem. Adv. Oper. Theory 4 (2019), no. 2, 529--538. doi:10.15352/aot.1809-1417. https://projecteuclid.org/euclid.aot/1543633242


Export citation

References

  • J. Delaporte and A. Derighetti, On Herz' extension theorem, Boll. Un. Mat. Ital. A (7) 6 (1992), no. 2, 245–247.
  • A. Derighetti, Convolution operators on groups, Lecture Notes of the Unione Matematica Italiana, 11. Springer, Heidelberg; UMI, Bologna, 2011.
  • C. Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 3, 91–123.
  • H. Reiter, Classical harmonic analysis and locally compact groups, Clarendon Press, Oxford, 1968.