Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

The transmutation operator for −d2/(w(x) dx2)

Amin Boumenira1

a1 Department of Mathematics, K.F.U.P.M. Dhahran, 31261, Saudia Arabia

Abstract

We would like to obtain the transmutation operator V, associated with the self-adjoint operators −d2/(w(x) dx2) and (−d2/(w(x) dx2)) + h(x), where w(x) ≎ xa as x → 0. We shall show that V = 1 + K, where K is a lower triangular Volterra operator.

(Received May 26 1993)

(Revised September 28 1993)