We establish a -Titchmarsh-Weyl theory for singular -Sturm-Liouville problems. We define -limit-point and -limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jackson -Bessel functions is given. This example leads to the completeness of a wide class of -cylindrical functions.
"-Titchmarsh-Weyl theory: Series expansion." Nagoya Math. J. 205 67 - 118, March 2012. https://doi.org/10.1215/00277630-1543787