the only such function is F(s) ■ Constant F , so that if K (s), K_0) 

 are one pair of factors, any other pair oust be of the form 



F o K. (s) , F" 1 K (s) . 

 o + o - 



In other words, a factorization with prescribed algebraic behavior at 



infinity is unique up to multiplication of K (s) by a constant F and 



division of K (s) by the same constant F . Mote the importance of the 



restriction to algebraic behavior at infinity. In many applications, 



part of K(s) can be represented as an infinite product from which the 



split K (s) K (s) can be effected by inspection. Usually, however, the 



infinite series of factors which gives K (s) or K_(s) has exponential 



behavior at infinity in R or R , and then it is necessary to divide 



say K (s) by an entire function with the nppiopriate exponential 



behavior at infinity in R. , so that the resulting factor behaves 

 + 



algebraically, at the same time multiplying IC (s) by the same factor 

 to eliminate exponential beliavior at infinity in R . Several examples 

 of this are given in the book by Noble [5]. 



19 



