On the equiconvergence of the eigenfunction expansion associated with certain 2nd order differential equations (Q1120042)

Let f,q be square integrable functions on \([0,+\infty)\). Consider the following boundary value problems: (1) \(-y''(x)=\lambda y(x),\) \(y(0)\cos a+y'(0)\sin a=0\) (2) \(-y''(x)+q(x)y(x)=\lambda y(x),\) \(y(0)\cos a+y'(0)\sin a=0\) where \(\lambda\) is a complex parameter and \(0\leq a<\pi\). The authors prove that if the eigenfunction expansion of f associated with (1) is convergent then so is the eigenfunction expansion of f associated with (2).