Ramanujan's master theorem and duality of symmetric spaces
The author studies Ramanujan's ``Master Theorem'', which consists of the formula \[ \int^\infty_0 x^{-s-1} \sum^\infty_{k=0} \bigl[(-1)^k a(k)x^k \bigr] dx= -{\pi \over \sin (\pi s)} a(s). \] He interprets this relation as one between Fourier transforms of an analytic function \(f\) with respect to the real forms \(U(1)\) (compact) and \(\mathbb{R}^+\) (noncompact) of the multiplicative group of non-zero complex numbers. The rank one case is treated in detail in the present paper.
scientific article; zbMATH DE number 1054125
scientific article