This article is cited in 9 papers

On a transformation operator

I. M. Guseinov

Baku State University

Abstract: 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.

UDC: 517.9

Received: 15.08.1995

DOI: 10.4213/mzm1605

 English version: Mathematical Notes, 1997, 62:2, 172–180

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