Abstract
Let H be a closed subgroup of G. We investigate the relations between \(CV_p(H)\ {\rm and}\ CV_p(G)\) and obtain noncommutative analogs of the relations between \(L^\infty(\hat{H})\ {\rm and}\ L^\infty(\hat{G})\). We prove that \(Res_HA_p(G)\ =\ A_p(H)\). We also generalize to noncommutative groups the Theorem of Kaplansky–Helson and basic results on sets of synthesis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Derighetti, A. (2011). Convolution Operators Supported by Subgroups. In: Convolution Operators on Groups. Lecture Notes of the Unione Matematica Italiana, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20656-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-20656-6_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20655-9
Online ISBN: 978-3-642-20656-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)