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Fourier analysis on semisimple symmetric spaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 880)

Keywords

  • Symmetric Space
  • Principal Series
  • Riemannian Symmetric Space
  • Principal Series Representation
  • Maximal Abelian Subspace

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References

  1. Berger, M.: Les espaces symétriques non compacts. Ann. Sci. École Norm. Sup., 74, 85–177(1957).

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  2. Flensted-Jensen, M.: Discrete series for semisimple symmetric spaces. Ann. of Math., 111, 253–311(1980).

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  3. Kashiwara, M. and Oshima, T.: Systems of differential equations with regular singularities and their boundary value problems. Ann. of Math., 106, 145–200(1977).

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  4. Matsuki, T.: The orbits of affine symmetric spaces under the action of the isotropy subgroups. J. Math. Soc. Japan, 31, 331–357(1979).

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  5. Oshima, T.: A realization of Riemannian symmetric spaces. J. Math. Soc. Japan, 30, 117–132(1978).

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  6. Oshima, T.: Poisson transformations on affine symmetric spaces. Proc. Japan Acad. Ser.A, 55, 323–327(1979).

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  7. Oshima, T. and Sekiguchi, J.: Eigenspaces of invariant differential operators on an affine symmetric space. Inv. Math., 57,1–81(1980).

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  8. Rosenberg, G.: A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group. Proc. A.M.S., 63, 143–149(1977).

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© 1981 Springer-Verlag

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Oshima, T. (1981). Fourier analysis on semisimple symmetric spaces. In: Carmona, J., Vergne, M. (eds) Non Commutative Harmonic Analysis and Lie Groups. Lecture Notes in Mathematics, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090416

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  • DOI: https://doi.org/10.1007/BFb0090416

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10872-6

  • Online ISBN: 978-3-540-38783-1

  • eBook Packages: Springer Book Archive