Some Relations between Stieltjes Transform and Hankel Transform with Applications

The Iterated Stieltjes Transform.

THEOREM 4. If Q is a Lie algebra of type All then n > 2 and $ SJ' where J is an i.a.a. of second kind in a simple algebra [. Thus a complete classification of Lie algebras of type A,, depends on the classification of simple associative algebras of second kind and of i.a.a.'s relative to cogredience in these algebras. It can be shown that the latter problem is essentially one of ordinary cogredi...

Extending the Stieltjes Transform

The classical Stieltjes transform is extended to a subspace of Boehmians. The transform is shown to be an analytic function in the half-plane Re z > 0. Some Abelian type theorems are established.

Quasiasymptotic Expansion of Distributions with Applications to the Stieltjes Transform

The Hankel transform

The Hankel Transform and Some of its Properties

The Hankel transform of an integer sequence is defined and some of its properties discussed. It is shown that the Hankel transform of a sequence S is the same as the Hankel transform of the Binomial or Invert transform of S. If H is the Hankel matrix of a sequence and H=LU is the LU decomposition of H, the behavior of the first super-diagonal of U under the Binomial or Invert transform is also ...