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OnL p spectral multipliers for a solvable lie group

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References

  1. G. Alexopoulos, A lower estimate for central probability on polycyclic groups, Can. J. Math. 44 (1987), 897–910.

    Google Scholar 

  2. G. Alexopoulos, Spectral multipliers on Lie groups of polynomial growth, Proc. AMS 120 (1994), 973–979.

    Google Scholar 

  3. J.-Ph. Anker,L p Fourier multipliers on Riemannian symmetric spaces of the non-compact type, Ann. of Math. 132 (1990), 597–628.

    Google Scholar 

  4. P. Bernat, N. Conze, et al. (Eds.), Représentations des groupes de Lie résolubles, Dunod, Paris, 1972.

    Google Scholar 

  5. J. Boidol, Connected groups with polynomially induced dual, J. Reine Angew. Math. 331 (1982), 32–46.

    Google Scholar 

  6. J.L. Clerc, E.M. Stein,L p-multipliers for non-compact symmetric spaces, Proc. Nat. Acad. Sci. USA 71 (1974), 3911–3912.

    Google Scholar 

  7. E. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.

    Google Scholar 

  8. M. Cowling, S. Giulini, A. Hulanicki, G. Mauceri, Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth, Studia Math. 111 (1994), 103–121.

    Google Scholar 

  9. S. Giulini, G. Mauceri, Analysis of distinguished Laplacians on solvable Lie groups, Math. Nachr. 163 (1993), 151–162.

    Google Scholar 

  10. W. Hebisch, The subalgebra ofL 1 (AN) generated by the Laplacian, Proc. Amer. Math. Soc. 117 (1993), 547–549.

    Google Scholar 

  11. W. Hebisch, Lecture given at Tuczno, Poland, July 1993.

  12. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Acad. Press, New York, 1978.

    Google Scholar 

  13. A. Hulanicki, Subalgebra ofL 1 (G) associated with Laplacians on a Lie group, Colloq. Math. 31 (1974), 259–287.

    Google Scholar 

  14. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966.

    Google Scholar 

  15. H. Leptin, D. Poguntke, Symmetry and nonsymmetry for locally compact groups, J. Functional Analysis 33 (1979), 119–134.

    Google Scholar 

  16. J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), 293–329.

    Google Scholar 

  17. E. Nelson, W. F. Stinespring, Representation of elliptic operators in an enveloping algebra, Amer. J. Math. 81 (1959), 547–560.

    Google Scholar 

  18. C. E. Rickart, Banach Algebras, Krieger Publishing Company, New York, 1960.

    Google Scholar 

  19. E.M. Stein, Topics in Harmonic Analysis, Princeton University Press, Princeton, NJ, 1970.

    Google Scholar 

  20. E.M. Stein, Harmonic Analysis, Princeton University Press, Princeton, NJ, 1993.

    Google Scholar 

  21. M.E. Taylor,L p-estimates on functions of the Laplace operator, Duke Math. J. 58 (1989), 773–793.

    Google Scholar 

  22. N.Th. Varopoulos, Diffusion on Lie groups, Can. J. Math. 46 (1994), 438–448.

    Google Scholar 

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Author notes

  1. Michael Christ

    Present address: Department of Mathematics, University of California, 94720, Berkeley, CA

Authors and Affiliations

  1. Department of Mathematics, UCLA, 90024-1555, Los Angeles, CA, USA

    Michael Christ

  2. Mathematisches Seminar, Christian-Albrechts Universität Kiel, Ludewig-Meyn Str. 4, 24098, Kiel, Germany

    Detlef Müller

Authors
  1. Michael Christ
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  2. Detlef Müller
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Additional information

Research supported by the International Center for the Mathematical Sciences, Edinburgh (both authors) and National Science Foundation grant DMS-9306833 (first author).

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Christ, M., Müller, D. OnL p spectral multipliers for a solvable lie group. Geometric and Functional Analysis 6, 860–876 (1996). https://doi.org/10.1007/BF02246787

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  • DOI: https://doi.org/10.1007/BF02246787

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