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Zeitschrift für Analysis und ihre Anwendungen


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Volume 23, Issue 4, 2004, pp. 731–743
DOI: 10.4171/ZAA/1219

Published online: 2004-12-31

On Representation, Boundedness and Convergence of Hankel-K{Mp}' Generalized Functions

Isabel Marrero[1]

(1) Universidad de La Laguna, Spain

Under opportune assumptions on the defining sequence $\{M_p\}_{p=0}^{\infty}$, Hankel-$K\{M_{p}\}'$ generalized functions can be represented as $$ f = x^{-\mu-\frac{1}{2}}(Dx^{-1})^kF(x), $$ where $k\in {\mathbb N}$ and $F$ is a continuous function on $I=(0,\infty)$ such that $M^{-1}_r F\in L^q(I)$ $(1\le q\le \infty)$ for some $r\in {\mathbb N}$. A corresponding characterization of boundedness and convergence of Hankel-$K\{M_{p}\}'$ generalized functions is given.

Keywords: Hankel transformation, Gelfand-Shilov spaces, generalized functions

Marrero Isabel: On Representation, Boundedness and Convergence of Hankel-K{Mp}' Generalized Functions. Z. Anal. Anwend. 23 (2004), 731-743. doi: 10.4171/ZAA/1219