An eigenfunction expansion of the non-selfadjoint Sturm-Liouville operator with a singular potential

作者：Arpat Esra Kir^*

来源：Journal of Mathematical Chemistry, 2013, 51(8): 2196-2213.

DOI：10.1007/s10910-013-0208-x

• Eigenvalues
• Spectral singularities
• Resolvent
• Spectral expansion

In this paper, we consider the operator generated in by the differential expression %26lt;br%26gt;l (y) =-y %26apos;%26apos; + [v(2)- 1/4/x(2) + q (x)] y, x is an element of R+ := (0, infinity) %26lt;br%26gt;and the boundary condition %26lt;br%26gt;lim(x -%26gt; 0)x(-v-1/2) y (x) = 1, %26lt;br%26gt;where is a complex valued function and is a complex number with Rev %26gt; 0 . We have proved a spectral expansion of L in terms of the principal functions under the condition %26lt;br%26gt;Sup(x is an element of R+) {e(epsilon root x) vertical bar q(x)vertical bar} %26lt; infinity, epsilon %26gt; 0 %26lt;br%26gt;taking into account the spectral singularities. We have also investigated the convergence of the spectral expansion.

• 出版日期2013-9