We prove that the Gelfand transform is a topological isomorphism between the space of polyradial Schwartz functions on the Heisenberg group and the space of Schwartz functions on the Heisenberg brush. We obtain analogous results for radial Schwartz functions on Heisenberg type groups.
Gelfand transforms of polyradial functions on the Heisenberg group
RICCI, Fulvio
2007
Abstract
We prove that the Gelfand transform is a topological isomorphism between the space of polyradial Schwartz functions on the Heisenberg group and the space of Schwartz functions on the Heisenberg brush. We obtain analogous results for radial Schwartz functions on Heisenberg type groups.File in questo prodotto:
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AstengoGelfand transforms of polyradial SchwartzJ. Funct. Anal.2007.pdf
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