The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

Details The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1 The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

2004-03-29

arxiv.org/abs/math-ph/0403056v1

Physics

Mathematical Physics

12 pages

Scientific paper

An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differential-geometric structure based on the classical Lagrange identity for a formally conjugated pair of differential operators. An extension of the method for the case of affine pencils of differential operators is suggested.

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