We interpret Ramanujan's Master Theorem (B. Berndt, ''Ramanujan's Note-books, Part I,'' Springer-Verlag, New York, 1985) integral(0)(infinity) x(-s-1) (k = 0)Sigma(infinity) ((-1)(k) a(k)x(k))dx = -pi/sin(pi s) a(s) (R) as a relation between the Fourier transforms of an analytic Function f with respect to the real forms U(1) (compact) and R+ (non-compact) of the multiplicative group of non-zero complex numbers, and we ask for a similar relation between the spherical Fourier transforms of an analytic function with respect to a compact real form and the non-compact dual real Form of a complex symmetric space. We obtained results in the case of symmetric cones and in the rank-one case. Here we present the latter case in detail, describing features which will be also important for the general rank case. (C) 1997 Academic Press. [References: 22]
展开▼
