On the Hankel transform of distributions

Distributional Chébli–Trimèche transforms

“…This paper can be seen as a continuation of [2]. However, we develop here a new idea, supported by the above mentioned representation for the elements of the dual space, that leads us to obtain easier proofs of the main properties of the distributional Chébli-Trimèche transform, in contrast with the proof for the corresponding properties for the distributional Hankel transforms presented in [9] and [11] and for the distributional Chébli-Trimèche transform established in [2]. Our procedure also works in other settings (see, for instance, distributional integral transforms defined in [18]).…”

“…Dube and Pandey [9], Koh and Zemanian [11] and Zemanian [18], amongst others, considered function spaces similar to H χ in their investigations about distributional integral transforms. …”

“…In this paper we define the distributional F transform by using the kernel method inspired in the ideas of Dube and Pandey [9] and Koh and Zemanian [11]. We obtain a representation of the elements of the corresponding dual spaces that allows us to get an explicit form for the distributional F transform.…”

The Meijer transformation of generalized functions

“…with the classical transformation whenever f is a regular distribution, that is, one that can be represented by a suitable integrable function. We note that there are various extensions of classical transforms in which the operational calculus is geared for other Bessel-type operators among which are the K-transform [3] and the Hankel transform [3], [4], [5] and [6].…”

An inversion of theS2transform for generalized functions

“…If G(u) is the Stieltjes transform of / e S' a (I) for u > 0, as defined by (3), it seems reasonable to define the iterated Stieltjes transform of / as , φeSJI).…”