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The Bicomplex Dual Fractional Hankel Transform

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We provide a concrete characterization of the Bergman space of bicomplex-valued bc-meromorphic functions with a strong pole at the origin of the bicomplex discus. The explicit expression of its reproducing kernel is given, and its integral representation as the range of the bicomplex version of the generalized second Bargmann transform is also considered. In addition, we construct the bicomplex analog of the fractional Hankel transform as well as its dual transform. Its range is described and its reproducing kernel is given. Such description involves the zeros of the generalized Laguerre polynomials.

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The author A.Hammam contributed to the entire manuscript. The main ideas that are developed by the author are characterizing the Bergman space of bicomplex-valued bc-meromorphic functions with a strong pole at the origin of the bicomplex discus. He studied the bicomplex extension of the generalized second Bargmann transform and then from that, he constructed the bicomplex fractional Hankel transform as well as its dual transform within some new properties.

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Correspondence to Adam Hammam.

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Communicated by Irene Sabadini

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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, and Daniele Struppa.

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Hammam, A. The Bicomplex Dual Fractional Hankel Transform. Complex Anal. Oper. Theory 18, 30 (2024).

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