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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 125, Issue 1
  • January 1995, pp. 85-98

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

  • Amin Boumenir (a1)
  • DOI:
  • Published online: 14 November 2011

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.

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1A. A. Boumenir . A comparison theorem for self-adjoint operators. Proc. Amer. Math. Soc. 111 (1991), 161175.

4M. A. Evgrafov and M. V. Fedoryuk . Asymptotic behaviour as λ→∞ of the solution of the equation w″–p(z, λ)w = 0 in the complex z-plane. Russian Math. Surveys 21 (1966), 149.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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