@article{García-Baquerín2024, 
author = {Samuel García-Baquerín and Isabel Marrero},
title = {Duals of Gelfand-Shilov spaces of type    K  {      M    p    } for the Hankel transformation},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {18247-18277},
keywords = {Bessel operator, boundedness, convergence, distribution, generalized function, K{Mp} space, representation, test function, Zemanian operator, Zemanian space},
url = {https://www.sciopen.com/article/10.3934/math.2024891},
doi = {10.3934/math.2024891},
abstract = {For    μ  ≥  −      1    2  , and under appropriate conditions on the sequence    {      M    p        }          p      =      0              ∞       of weights, the elements, the (weakly, weakly*, strongly) bounded subsets, and the (weakly, weakly*, strongly) convergent sequences in the dual of a space              K        μ   of type Hankel-   K  {      M    p    } can be represented by distributional derivatives of functions and measures in terms of iterated adjoints of the differential operator        x          −      1            D    x   and the Bessel operator        S    μ    =      x          −      μ      −              1        2                  D    x        x          2      μ      +      1            D    x        x          −      μ      −              1        2            . In this paper, such representations are compiled, and new ones involving adjoints of suitable iterations of the Zemanian differential operator        N    μ    =        x          μ      +              1        2                  D    x        x          −      μ      −              1        2             are proved. Prior to this, new descriptions of the topology of the space              K        μ   are given in terms of the latter iterations.}
}