Abstract
We deal with a class of one-parameter family of integral transforms of Bargmann type arising as dual transform of fractional Hankel transform. Their ranges are identified to be special subspaces of the weighted hyperholomorphic left Hilbert spaces, generalizing the slice Bergman space of the second kind. Their reproducing kernel is given by closed expression involving the ⋆-regularization of Gauss hypergeometric function. We also discuss their basic properties such as boundedness and we determine their singular values. Moreover, we describe their compactness and membership in p-Schatten classes. The operational calculus for this transform is also investigated.
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Acknowledgments
The author would like to thank the anonymous referees for helpful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).