Basic Properties of Toeplitz Operatorsin Other (Other) by Dgoodz19
Your Price: $15.00 (30% discount)
You Save: $6.43
88 2 The Unilateral Shift and Factorization of Functions
Now we can nally prove that functions of the above form are outer.
Theorem . If f is in H 2 and F is dened by
2 i 1 e z F (z) exp log f (ei ) d , 2 0 ei z
then F is outer. Proof. It was shown above (Theorem ) that F is in H 2 . Thus F G for an inner function and G an outer function (Theorem ). It suces i ) 1 a.e., it follows that to show that is a constant function. Since (e F(ei ) ...