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Proceedings of the American Mathematical Society

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Primary summand functions on three-dimensional compact solvmanifolds

Author: Carolyn Pfeffer
Journal: Proc. Amer. Math. Soc. 116 (1992), 213-217
MSC: Primary 22E25; Secondary 22E40
MathSciNet review: 1112499
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Abstract: Leonard Richardson has shown that for a certain class of three-dimensional compact solvmanifolds, projections onto $ \pi $-primary summands of $ {L^2}\left( M \right)$ do not preserve the continuity of functions on $ M$. It is shown here that if the $ \pi $-primary projection of a continuous function is $ {L^\infty }$ then it is actually continuous. From this it follows that there are continuous functions on $ M$ whose $ \pi $-primary projections are essentially unbounded.

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  • [AGH] L. Auslander, L. Green, and F. Hahn, Flows on homogeneous spaces, Ann. Math. Stud., no. 53, Princeton Univ. Press, Princeton, NJ, 1963.
  • [AB] L. Auslander and J. Brezin, Uniform distribution in solvmanifolds, Advances in Math. 7 (1971), 111–144. MR 0301137
  • [B] Jonathan Brezin, Geometry and the method of Kirillov, Non-commutative harmonic analysis (Actes Colloq., Marseille-Luminy, 1974), Springer, Berlin, 1975, pp. 13–25. Lecture Notes in Math., Vol. 466. MR 0387484
  • [CG] Lawrence J. Corwin and Frederick P. Greenleaf, Representations of nilpotent Lie groups and their applications. Part I, Cambridge Studies in Advanced Mathematics, vol. 18, Cambridge University Press, Cambridge, 1990. Basic theory and examples. MR 1070979
  • [GGP] I. M. Gel′fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Representation theory and automorphic functions, Translated from the Russian by K. A. Hirsch, W. B. Saunders Co., Philadelphia, Pa.-London-Toronto, Ont., 1969. MR 0233772
  • [H] James E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York-Berlin, 1972. Graduate Texts in Mathematics, Vol. 9. MR 0323842
  • [Ril] Leonard F. Richardson, A class of idempotent measures on compact nilmanifolds, Acta Math. 135 (1975), no. 1-2, 129–154. MR 0486324
  • [Ri2] Leonard F. Richardson, 𝑁-step nilpotent Lie groups with flat Kirillov orbits, Colloq. Math. 52 (1987), no. 2, 285–287. MR 893545
  • [Ru] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR 0152834
  • [Z] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776

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Article copyright: © Copyright 1992 American Mathematical Society