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Integral Transforms Related to a Generalized Convolution

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Abstract

Integral transformations of the form from Lp(ℝ+) into Lq(ℝ+); (1 ≤ p ≤ 2, p−1 + q −1 = 1) are studied. Necessary and sufficient conditions on k to ensure that the transformation is unitary on L2(ℝ+) are obtained, and a formula for the inverse transformation is derived in this case.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait

    F. Al-Musallam & Vu Kim Tuan

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  1. F. Al-Musallam
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  2. Vu Kim Tuan
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Correspondence to F. Al-Musallam.

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Al-Musallam, F., Tuan, V.K. Integral Transforms Related to a Generalized Convolution. Results. Math. 38, 197–208 (2000). https://doi.org/10.1007/BF03322007

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  • DOI: https://doi.org/10.1007/BF03322007

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