Abelian theorems for Whittaker transforms

Mellin transforms of Whittaker functions

In this note we show that for an arbitrary semisimple Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We determine the possible poles.

Mellin transforms of p-adic Whittaker functions

Tauberian Theorems for Summability Transforms

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...

Some Finiteness Theorems for Abelian Varieties

Last time we saw (see Proposition 6.5 in those lecture notes) that an abelian variety A of dimension g over K, the fraction field of a henselian dvr R, acquires semistable reduction over K(A[`]) for ` equal to 4 or an odd prime, with ` not divisible by the residue characteristic. (The same circle of ideas yielded the non-obvious fact that over K the intersection of two “semistable field extensi...

Similarity theorems for fractional Fourier transforms and fractional Hankel

The significance of the similarity theorem for the fractional Fourier transform is discussed, and the properties of self-similar functions considered. The concept of the fractional Hankel transform is developed for use in the analysis of diffraction and imaging in symmetrical optical systems. The particular case of Fresnel diffraction from a circular aperture is discussed and the effects of the...