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wu :: forums    general    complex analysis (Moderators: ThudnBlunder, Icarus, towr, SMQ, william wu, Eigenray, Grimbal)    Cplx Problem « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Cplx Problem  (Read 2691 times) axterix Guest Cplx Problem   « on: Jul 22nd, 2005, 4:15pm » Quote Modify Remove Find all function f analytic in the disk D such that |z| < R which satisfies f(0) = i and |f(z)| <=1 or all z in D, and where R is any number greater than zero. IP Logged Michael Dagg Senior Riddler     Gender: Posts: 500 Re: Cplx Problem   « Reply #1 on: Jul 23rd, 2005, 9:01am » Quote Modify This problem slightly misstated. There is only one such function and it is f(z) = i.   IP Logged Regards, Michael Dagg axterix Guest Re: Cplx Problem   « Reply #2 on: Jul 26th, 2005, 9:21pm » Quote Modify Remove That is the right answer but what part is wrong? IP Logged axterix Guest Re: Cplx Problem   « Reply #3 on: Jul 26th, 2005, 9:36pm » Quote Modify Remove Ah, never mind - I see it.   How do you know or how did show that there is only one function f(z) = i that satisfies the properties? IP Logged Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Cplx Problem   « Reply #4 on: Jul 27th, 2005, 10:56am » Quote Modify Read up on the maximum modulus principle.  Or the open mapping theorem. IP Logged Michael Dagg Senior Riddler     Gender: Posts: 500 Re: Cplx Problem   « Reply #5 on: Jul 27th, 2005, 12:04pm » Quote Modify The problem is a frequent exercise in CA books and is generally associated with the first hint Eigenray gave. IP Logged Regards, Michael Dagg Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth => complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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