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Integral Representations of Bargmann Type for the \(\beta \)-Modified Bergman Space on Punctured Unit Disc

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Abstract

We deal with the integral representation of Bargmann type of the functions belonging to the \(\beta \)-modified Bergman space on the punctured unit disc, by means of some special kernel-distribution involving the confluent hypergeometric functions and generalizing the classical second Bargmann transform. As application, we derive integral formula on the unit disc for the product of confluent hypergeometric functions, by considering the associated fractional Hankel transform.

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Authors and Affiliations

  1. Analysis, P.D.E. and Spectral Geometry, Lab. MIA-S.I., CeReMAR, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, P.O. Box 1014, Rabat, Morocco

    Allal Ghanmi

  2. Department of Mathematics, Faculty of Sciences, University of Gabes, 6072, Gabes, Tunisia

    Safa Snoun

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  1. Allal Ghanmi
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  2. Safa Snoun
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Correspondence to Allal Ghanmi.

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Communicated by Jerry R. Muir.

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Ghanmi, A., Snoun, S. Integral Representations of Bargmann Type for the \(\beta \)-Modified Bergman Space on Punctured Unit Disc. Bull. Malays. Math. Sci. Soc. 45, 1367–1381 (2022). https://doi.org/10.1007/s40840-022-01244-w

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  • DOI: https://doi.org/10.1007/s40840-022-01244-w

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