128 BIRKHOFF AND LANGER. 



T(x)- = \A(x)\ + B(x)}Y(x)-, 

 WaY(a)-+W b Y(b)~ = 0, 



which can be reduced by a change of the dependent variable to a 

 system of type (46) for which (a), R(x) and B(x) are continuous to- 

 gether with their first derivatives (t),thefunctions 7j(a*), i = 1,2, . . .n t 

 satisfy the relations (96) and (97), and (c), the condition (ii) on page 

 89 is fulfilled. Then the development in characteristic functions of the 

 system L which is associated with any vector F(x) • whose elements 

 satisfy condition (98), converges to 



\ F(x - 0) • + i F(x + 0) • when x 4= a, x + b, 

 H a F(a + 0) • + J a F(b - 0) • when x = a, 

 H b F(a + 0) • + J b F(b - 0) • when x = b, 



the four matrices of constants H a , J a , H b , and J b being explicitly 

 determined by the matrices R(x), A(x), W„ and W b as stated. 



