math185-hw7sol - MATH 185 COMPLEX ANALYSIS FALL 2007\/08 PROBLEM SET 7 SOLUTIONS As in the lectures for an a D(0 1 we will write a for the function

# math185-hw7sol - MATH 185 COMPLEX ANALYSIS FALL 2007/08...

• Notes
• mjg68
• 4

This preview shows page 1 - 3 out of 4 pages.

MATH 185: COMPLEX ANALYSIS FALL 2007/08 PROBLEM SET 7 SOLUTIONS As in the lectures, for an a D (0 , 1), we will write ϕ a for the function defined by ϕ a ( z ) = z - a 1 - az . 1. Let f : C C be an entire function. Show that if | f ( z ) | ≤ 1 | Re z | for all z C , then f 0. What happens if we replace the condition by | f ( z ) | ≤ 1 | Im z | for all z C ? Solution. This is of course almost identical to Proposition 7.3 in the text and an almost identical proof works. Let R > 0. Consider the function

#### You've reached the end of your free preview.

Want to read all 4 pages?

• Fall '07
• Lim
• Math, GB, maximum modulus theorem, ωB

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern