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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Harmonic analysis on nilmanifolds
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by Jonathan Brezin PDF
Trans. Amer. Math. Soc. 150 (1970), 611-618 Request permission

Abstract:

We compute, using a device of A. Weil, an explicit decomposition of ${L^2}$ of a nilmanifold into irreducible translation-invariant subspaces. The results refine previous work of C. C. Moore and L. Green.
References
    L. Auslander, On a problem of Philip Hall, Ann. of Math. (2) 86 (1967), 112-116. MR 36 #1540. L. Auslander et al., Flows on homogeneous spaces, Ann. of Math. Studies, No. 53, Princeton Univ. Press, Princeton, N. J., 1963, Chapter V. MR 29 #4841. A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4(106), 57-110. (Russian) MR 25 #5396. C. C. Moore, Decomposition of unitary representations defined by discrete subgroups of nilpotent groups, Ann. of Math. (2) 82 (1965), 146-182. MR 31 #5928. J. Scheuneman, Two-step nilpotent Lie algebras, J. Algebra 7 (1967), 152-159. MR 36 #225. A. Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143-211. MR 29 #2324.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 150 (1970), 611-618
  • MSC: Primary 22.65
  • DOI: https://doi.org/10.1090/S0002-9947-1970-0279244-3
  • MathSciNet review: 0279244