Geodesic
Representations of Inverse Functions by the Integral Transform with the Sign Kernel
Fractional calculus and applied analysis, Tome 10 (2007) no. 2, pp. 161-168.

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In this paper we give practical and numerical representations of inverse functions by using the integral transform with the sign kernel, and show corresponding numerical experiments by using computers. We derive a very simple formula from a general idea for the representation of the inverse functions, based on the theory of reproducing kernels.
Keywords: Inverse Function, Reproducing Kernel, Sobolev Space, Sign Function, Integral Transform, Solution Method of General Equations, 30C40 
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Yamada, Masato; Matsuura, Tsutomu; Saitoh, Saburou. Representations of Inverse Functions by the Integral Transform with the Sign Kernel. Fractional calculus and applied analysis, Tome 10 (2007) no. 2, pp. 161-168. http://geodesic.mathdoc.fr/item/FCAA_2007_10_2_a5/