Skip to main content
Log in

A Fourier transform for compact nilmanifolds with flat orbits

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Auslander, L., Brezin, J.: Uniform distributions on solvmanifolds. Adv. Math.7, 111–144 (1971).

    Google Scholar 

  2. Benedek, A., Panzone, R.: The spacesL p, with mixed norm. Duke Math. J.28, 301–324 (1961).

    Article  Google Scholar 

  3. Bourbaki, N.: Integration, Chap. 7 et 8, Act. Sc. Ind. No. 1306. Paris: Hermann 1963

    Google Scholar 

  4. Brezin, J.: Geometry and the method of Kirillov. In: Non-commutative harmonic analysis. Lect. Notes Math. Vol. 466. Berlin, Heidelberg, New York: Springer 1975.

    Google Scholar 

  5. Brezin, J.: Harmonic analysis on compact solvmanifolds. Lect. Notes Math. Vol. 602. Berlin. Heidelberg, New York: Springer 1977

    Google Scholar 

  6. Corwin, L., Greenleaf, F.P.: Character formulas and spectra of compact nilmanifolds. J. Funct. Anal.21, 123–154 (1976).

    Google Scholar 

  7. Corwin, L., Greenleaf, F.P.: Integral formulas with distribution kernels for irreducible projections inL 2 of a nilmanifold. J. Funct. Anal.23, 255–284 (1976).

    Google Scholar 

  8. Corwin, L., Greenleaf, F.P., Penney, R.: A canonical formula for the distribution kernel of primary projections inL 2 of a nilmanifold. Commun. Pure Appl. Math.30, 355–372 (1977).

    Google Scholar 

  9. Gangolli, R.: Spectra of discrete uniform subgroups of semi-simple Lie group. In Symmetric spaces. Short courses presented at Washington University. New York: Dekker 1972.

    Google Scholar 

  10. Gel'fand, I.M., Graev, M.I., Pyatetskii-Shapiro, I.I.: Representation theory and automorphic functions. Philadelphia: Saunders 1969

    Google Scholar 

  11. Hewitt, E., Ross, K.A.: Abstract harmonic analysis, Vol. I, second edition. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  12. Hewitt, E., Ross, K.A.: Abstract harmonic analysis. Vol. II. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  13. Howe, R.: On Frobenius reciprocity for unipoten algebraic groups overQ. Am. J. Math.93, 163–172 (1971)

    Google Scholar 

  14. Kirillov, A.A.: Unitary representations of nilpotent Lie groups. Usp. Mat. Nauk17 (1962) 57–110 (=Russ. Math. Sur.17, 53–104, (1962)

    Google Scholar 

  15. Lipsman, R.L.: Group representation. Lect. Notes Math. Vol. 388. Berlin, Heidelberg, New York: Springer 1974

    Google Scholar 

  16. Moore, C.C., Wolf, J.A.: Square integrable representations of nilpotent groups. Trans. Am. Math. Soc.185, 445–462 (1973)

    Google Scholar 

  17. Penney, R.: Square integrable representations and nilmanifolds. J. Funct. Anal.42, 121–127 (1981)

    Google Scholar 

  18. Richardson, L.F.: Decomposition of theL 2-space of a general compact nilmanifold. Am. J. Math.93, 173–190 (1971)

    Google Scholar 

  19. Richardson, L.F.: A class of idempotent measures on compact nilmanifolds. Acta Math.135, 129–154 (1975)

    Google Scholar 

  20. Richardson, L.F.: Fejer's theorem on nilmanifolds with flat orbits (preprint)

Download references

Author information

Authors and Affiliations

Authors

Additional information

Some of this work was done while the second author was visiting Queen's University at Kingston. He would like to thank the Natural Sciences and Engineering Research Council of Canada and the Advisory Research Council of Queen's University for their financial support

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nielsen, O.A., Rains, M. A Fourier transform for compact nilmanifolds with flat orbits. Math. Ann. 271, 209–223 (1985). https://doi.org/10.1007/BF01455987

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01455987

Keywords

Navigation