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Titlebook: Hyperfunctions and Harmonic Analysis on Symmetric Spaces; Henrik Schlichtkrull Book 1984 Birkhäuser Boston, Inc. 1984 Microlocal analysis.

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Boundary values on the full boundary,G/K has rank < 1 this is, however, only a small part of the boundary of G/K in X̃, and it is important to have analogous results for the other G-orbits in the boundary. In this chapter we therefore generalize the results of Chapter 5 to this situation.
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Construction of functions with integrable square,nique up to scalars. Hence the Hilbert space L. (G/H) makes sense, and we can study the unitary representation . (g,x . G) of G on this space. It is the purpose of L.-harmonic analysis on G/H to give an explicit decomposition (in general as a direct integral) of this representation into irreducibles
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Progress in Mathematicshttp://image.papertrans.cn/h/image/430632.jpg
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A compact imbedding,Let X be a Riemannian symmetric space. It is the purpose of this chapter to construct an imbedding of X into a compact real analytic manifold X̃. For the study of the asymptotic behavior of functions on X, which we shall carry out in the next chapters, this is of crucial importance.
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Boundary values and Poisson integral representations,Consider the open disk D = {|z| > 1} in . with the boundary T = {|z| = 1}. The classical Poisson kernel is defined by . for z . D , t . T , and the Poisson transform .f on D of a function f on T is given by
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