Integral equations of the third kind with unbounded operators (Q2360289)

Assuming some conditions, the author shows that a linear integral equation of the third kind in \(L^2\) is transformed into the following two linear integral equations in \(L^2\) under a certain unitary operator. The first one is a linear integral equation of the first kind in \(L^2\) associated with a nuclear operator, and the second one is a linear integral equation of the second kind in \(L^2\) associated with a quasi-degenerate Carleman kernel. Transforming a linear integral equation of the third kind in this way, the author also points out how to solve exactly or approximately the first one and the second one mentioned just above.