AM  Vol.5 No.19 , November 2014
Amenability and the Extension Property
ABSTRACT
Let G be a locally compact group, H a closed amenable subgroup and u an element of the Herz Figà-Talamanca algebra of H with compact support, we prove the existence of an extension of u to G, with a good control of the norm and of the support of the extension.

Cite this paper
Derighetti, A. (2014) Amenability and the Extension Property. Applied Mathematics, 5, 2945-2951. doi: 10.4236/am.2014.519279.
References
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http://dx.doi.org/10.5802/aif.473

[2]   Fiorillo, C. (2009) An Extension Property for the Figà-Talamanca Herz Algebra. Proceedings of the American Mathematical Society, 137, 1001-1011.
http://dx.doi.org/10.1090/S0002-9939-08-09679-2

[3]   McMullen, J.R. (1972) Extensions of Positive-Definite Functions. Memoirs of the American Mathematical Society, 117.

[4]   Delaporte, J. and Derighetti, A. (1992) On Herz’ Extension Theorem. Bollettino dell’Unime Matematica Italiana, (7) 6-A, 245-247.

[5]   Reiter, H. and Stegman, J.D. (2000) Classical Harmonic Analysis and Locally Compact Groups. Clarendon Press, Oxford.

[6]   Derighetti, A. (2004) On Herz’s Projection Theorem. Illinois Journal of Mathematics, 48, 463-476.

[7]   Derighetti, A. (2011) Convolution Operators on Groups. Lecture Notes of the Unione Matematica Italiana, 11, Springer-Verlag, Berlin, Heidelberg.

[8]   Delaporte, J. and Derighetti, A. (1995) p-Pseudomeasures and Closed Subgroups. Monatshefte für Mathematik, 119, 37-47.
http://dx.doi.org/10.1007/BF01292767

 
 
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