Abstract
The construction of integro-differential transmutation operators for the Sturm-Liouville equation in impedance form is presented. Their analytical properties of boundedness and invertibility in appropriate functional spaces are studied. A Fourier-Legendre series for the integral transmutation kernel in terms of the Legendre polynomials is obtained together with a representation of the solutions of the Sturm-Liouville equation in impedance form as Neumann series of Bessel functions.
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