Abstract
It follows from the polar decomposition G = K Cl(A+)K that any K-biinvariant function on G is essentially determined by its restriction to A+. Suppose D is a K-biinvariant C∞ differential operator on G. Then one can set up “polar coordinates” on the open set G+ = KA+K and determine a C∞ differential operator \(\tilde D\) on A+ such that, for all \(f \in c^\infty (G//k)\)
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© 1988 Springer-Verlag Berlin Heidelberg
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Gangolli, R., Varadarajan, V.S. (1988). The Harish-Chandra Series for φ λ and the c-Function. In: Harmonic Analysis of Spherical Functions on Real Reductive Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72956-0_4
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DOI: https://doi.org/10.1007/978-3-642-72956-0_4
Publisher Name: Springer, Berlin, Heidelberg
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