fi[O, 1], then I zp"(z) + 4zp'(z) + 2p(z)-I < (M- Ip(z) I <

EXAMPLE 2.4m. Let A, B, C and D be complex-valued functions defined on U that satisfy

(2.4-7) {

and a = 1. We first show that 'I' E '¥ n { 1 } , by showing that admissibility condition (2.3-11) is satisfied. This follows since

when ~ :$ - [1 + p 2 ]/2. The second condition in (2.4-7) implies that this last quadratic will be less than or equal to zero. Therefore (2.3-11) is

satisfied and by Theorem 2.3i we obtain the following result:

If p E .)J [ 1 , n] , and A, B, C and D satisfy (2.4-7), then