Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations by Audrey Terras

Author:Audrey Terras
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(d)Now suppose that has the Fourier expansion:

if W is expressed as in part (b). Show that

where τ = k(m − k) + 1 and the integral is over , t ≥ 1, u ≥ 0.

(e)What hypotheses on f are necessary to justify the preceding arguments? Be careful. It was just this sort of divergent integral problem that led to gaps in many papers, as we mentioned in the remarks on part (5) of Theorem 1.5.2 in Section 1.5.2.

(f)In the special case , the Eisenstein series from formula (3.81) of Section 3.5, Volume I and Exercise 1.5.2 of Section 1.5.1, let

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