Convolutions, Spherical Functions and the Mellin Transform
We shall study integral operators, but these are not independent of the differential operators. We begin by formulating a general result which applies to both. There are other relations showing that eigenvalues of certain differential operators are also eigenvalues of certain integral operators. The chapter concerns the work of Gelfand [Gel 50], Godement [God 52b], Maass [Maa 55], [Maa 56], [Maa 71], and Selberg [Sel 56], especially pp. 48–58.
KeywordsSymmetric Space Haar Measure Spherical Function Point Pair Absolute Convergence
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