15.6 Find all functions f which are holomorphic in D(0; 1) and such the f(1/n) n2f (1/n)3 for n 2...
(3) 5. Suppose that f : D[0, 1] → D[0, 1] is holomorphic, prove that f'(2) < 1/(1 - 121) for all z e D[0,1].
[3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that \f'(x) < 1/(1 - 1z| for all z e D[0, 1]. [3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that f'(x) < 1/(1-1-12 for all z e D[0, 1]
[3] 5. Suppose that f: D[0, 1] → D[0, 1] is holomorphic, prove that [f'(x) = 1/(1 – )2 for all z e D[0, 1].
[3] 5. Suppose that f: D[0,1] for all z E D[0, 1] D[0,1] is holomorphic, prove that \f'(z) < 1/(1 - 121)2
.Suppose that f : D[0, 1] → D[0, 1] is holomorphic, prove that |f 0 (z)| ≤ 1/(1 − |z|) ^2 for all z ∈ D[0, 1]. is there any way not to use the Schwartz' lemma
[3] 5. Suppose that f: D[0,1] for all z E D(0,1) D[0,1] is holomorphic, prove that f'() 5 1/(1 - 121)?
Let f be a function which is holomorphic on the unit disk D (0). We define the quantity R= sup \f (2) - f(w) ) ED (0) ( (which can be infinite). 1. Prove that Vr € (0,1), 2f'(0) = 2 1 f6)-f(-) .0) (2 where the circle C,(0) is traversed in the counterclockwise direction 2. Deduce from the previous result that 28' (O SR.
12. Let D = {2E C | 너く1} denote the open unit disc and let f : D → C be a holomorphic function. Suppose that for any integer n>1 we have that f(1/n)-1/n3. Show that f(z)3.
12. Let D = {2E C | 너く1} denote the open unit disc and let f : D → C be a holomorphic function. Suppose that for any integer n>1 we have that f(1/n)-1/n3. Show that f(z)3.
7. Find a holomorphic function F(z) on Ω-z I Izl < r} such that for any a E Ω, F(a) F(0)-da. 0
7. Find a holomorphic function F(z) on Ω-z I Izl
2. Which of the following recursive functions, written in a fictitious language, are tail recursive? Select all that are A. function f(n) ifn<2 else f(n-1) + f(n-2) end If m=0 else B. function g(m,n) g(m-1,m'n) C. function h(n) if n 100 else 3 h(n+5) end D. function j(m.n) IT m=n 100 j(m-n,n) 10 j(n,n-m) elseif mn else
2. Which of the following recursive functions, written in a fictitious language, are tail recursive? Select all that are A. function f(n) ifn