Carleman boundary value problems and boundary value problems of Carleman type

Abstract

If we suppose that limit values of the same unknown function are conjugated in the boundary value conditions (8.2) and (8.3), then we obtain two more binomial boundary value problems with a shift:

$$ \Phi ^ + \left( {\alpha _ - \left( t \right)} \right) = G\left( t \right)\Phi ^ + \left( t \right) + g\left( t \right) $$

(I3)

,

$$ \Phi ^ + \left( {\alpha_ - \left( t \right)} \right) = G\left( t \right)\overline {\Phi ^ + \left( t \right)} + g\left( t \right) $$

(II3)

. Problem (I₃) is called a Carleman boundary value problem. We shall refer to problem (II₃) as a boundary value problem of Carleman type, using a similar terminology to the one we have used in relation to the problems (7.1) and (8.1).