Geodesic
On a transformation operator
Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 206-215 
I. M. Guseinov. On a transformation operator. Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 206-215. http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a4/
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     title = {On a transformation operator},
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     year = {1997},
     volume = {62},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the existence of a transformation operator that takes the solution of the equation $y''=\lambda^{2n}y$ to the solution of the equation $$ y''-\bigl(q_0(x)+\lambda q_1(x)+\dots+\lambda^{n-1}q_{n-1}(x)\bigr)y=\lambda^{2n}y $$ with a condition at infinity. Some properties of the kernel of this operator are studied.

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