An outline of the results of this paper (with the exception of Ch.II, w 4 and Ch.IV, w167 5-8) was given [25] at the Scandinavian Mathematical Congress in Helsinki, August 1957.An exposition was given in a course at the University of Chicago, Spring 1958.I am grateful to Professor/i~sgeirsson for advice concerning some problems dealt with in Chapter IV, w 3. I am also grateful to Professor Harish-Chandra for interesting conversations about the topic of his paper [21].
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Sigurđur Helgason (1959) studied this question.