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Article

González, Benito J. ; Negrin, Emilio R.
The link between the kernel method and the method of adjoints for the generalized index $_2F_1$-transform. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 37 (1996), issue 4, pp. 691-694
MSC: 44A15, 46F12 | MR 1440701 | Zbl 0896.46028
Keywords:
index transform; hypergeometric function; distributions of compact support
Summary:
In this note we show that the two definitions of generalized index ${ }_{2}F_{1}$-transform given in the previous works [1] and [2] agree for distributions of compact support.
References:
[1] Hayek N., González B.J.: The index $ _{2}F_{1}$-transform of generalized functions. Comment. Math. Univ. Carolinae 34.4 (1993), 657-671. MR 1263795
[2] Hayek N., González B.J.: On the distributional index $ _{2}F_{1}$-transform. Math. Nachr. 165 (1994), 15-24. MR 1261360
[3] Lisena B.: On the Generalized Kontorovich-Lebedev Transform. Rend. Math. Appl. (7) 9 (1989), 87-101. MR 1044519 | Zbl 0733.46019
[4] Prudnikov A.P., Brychkov Y.A., Marichev O.I.: Integrals and Series. vol. 3, Gordon and Breach Science Publishers, New York, 1990. MR 1054647 | Zbl 1103.33300
[5] Treves F.: Topological Vector Spaces, Distributions and Kernels. Academic Press, New York, 1967. MR 0225131 | Zbl 1111.46001
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