Recent content by jinsing

  1. J

    Prove f is constant - liouville's theorem (?)

    That's perfect. Thank you very much you guys!
  2. J

    Prove f is constant - liouville's theorem (?)

    Or, rather, how'd you get 1/(f(z)-i)?
  3. J

    Prove f is constant - liouville's theorem (?)

    gopher p: no I can't use Little Picard, unfortunately. I looked it up, though, and it did seem pretty helpful! Thanks for the suggestion! Citan Uzuki: yeah, that's what I thought.. my method definitely seemed a tad suspicious to me. I don't quite understand how 1/(f(z)-i) would help.. could you...
  4. J

    Prove f is constant - liouville's theorem (?)

    I hate to be this guy.. but does this look okay? I still need help..
  5. J

    Prove f is constant - liouville's theorem (?)

    Homework Statement Let f=u+iv, where u(z)>v(z) for all z in the complex plane. Show that f is constant on C. Homework Equations none The Attempt at a Solution Here's my attempt (just a sketch): Since f is entire, then its components u(z), v(z) are also entire <- is this...
  6. J

    Probably easy Laurent expansion question

    Ah, that's what I thought, I was just doubting myself.. thanks so much for the help!
  7. J

    Probably easy Laurent expansion question

    Maybe there is no Laurent expansion since the series doesn't converge?
  8. J

    Probably easy Laurent expansion question

    Okay, so I expand 1/z = 1/((z-3)+3) = (1/(z-3)) * (1/(1-(-3/(z-3))) = 1 - 3/(z-3) + 9/(z-3)^2 - 27/(z-3)^3 + ... Is this right? My issue keeps coming up with a way to use the geometric series while keeping |c|<1 (if 1/(1-c) = 1+c+c^2+...) I think the answer requires that c= (z-3)/3 ..how...
  9. J

    Probably easy Laurent expansion question

    Okay.. so now I have: ((1/9z) - (1/9(z-3)) + 1/(3(z-3)^2))(1/z) I'm probably missing something completely obvious, but I'm still stuck at where I was before..
  10. J

    Probably easy Laurent expansion question

    Homework Statement Find the Laurent expansion of f(z)= 1/(z^3 - 6z^2 + 9z) in the annulus |z-3|>3. Homework Equations none The Attempt at a Solution I've been spending way too long on this problem.. I can't seem to think of a way to manipulate f to use the geometric series, other...
  11. J

    Liouville's theorem - (probably) easy question

    Ah, got it! Thank you so much!
  12. J

    Liouville's theorem - (probably) easy question

    Would that involve looking at the Cauchy differentiation formula and using the maximum*length principle? Is it because f is entire we know we can use CDF? In other words, do we know there exists a z_0 inside a simple closed curve gamma such that CDF holds because f is entire?
  13. J

    Liouville's theorem - (probably) easy question

    Homework Statement If f is an entire function and |f(z)|\leq C|z|^(1/2) for all complex numbers z, where C is a positive constant, show that f is constant. Homework Equations All bounded and entire functions are constant. The Attempt at a Solution I'm 99% sure this can be easily...
  14. J

    Is Infimum of Non-Negative Measurable Functions Non-Negative Almost Everywhere?

    Ah! Thanks for the input!
  15. J

    Is Infimum of Non-Negative Measurable Functions Non-Negative Almost Everywhere?

    Homework Statement If {f_n} is a collection of measurable functions defined on R and satisfying: |f_n(x)|<= 1 for all n in N and x in R and f_n(x) >=0 almost everywhere on R for all n in N and f(x) = inf{f_n(x)|n in N}, then f(x) >= 0 almost everywhere on R. Homework Equations Almost...