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Changes of Variables Preserving Fourier-Stieltjes Transforms on Simply Connected Nilpotent Lie Groups

Published online by Cambridge University Press:  20 November 2018

S. W. Drury
S. W. Drury*
Affiliation:
McGill University, Montreal, Quebec
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In [1] Beurling and Helson prove the following theorem.

THEOREM. Let φ: R → R be a continuous map such that

Then φ is affine. (Here denotes the space of Fourier-Stieltjes transforms on R.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 744 - 755
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Beurling, A. and Helson, H., Fourier-Stieltjes transforms with bounded powers, Math. Scand. 1 (1953), 120–126.Google Scholar
2. Eymard, P., L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236.Google Scholar
3. Jacobson, N., Lie algebras, Interscience tracts in pure and applied mathematics No. 10 (New York, 1962).Google Scholar