MR1992
Reputation
Next privilege 75 Rep.
Set bounties
 Jul2 awarded Curious Feb7 comment Prove partial derivatives of uniformly convergent harmonic functions converge to the partial derivative of the limit of the sequence. Hello. I'm unfamiliar with L norms. I'm learning about harmonic functions in a one variable complex analysis course. I was wondering if you could elaborate on how you derived the given inequality. I'm still unsure of where divergence theorem comes in. I think I was able to derive the Cauchy integral formula for harmonic functions but the formula for derivative I'm getting seems to be the same for all the partial derivatives... Feb7 asked Prove partial derivatives of uniformly convergent harmonic functions converge to the partial derivative of the limit of the sequence. Jan21 accepted Prove that the orbit of an iterated rotation of 0 (by (A)(Pi), A irrational) around a circle centered at the origin is dense in the circle. Jan19 awarded Supporter Jan19 asked Prove that the orbit of an iterated rotation of 0 (by (A)(Pi), A irrational) around a circle centered at the origin is dense in the circle. Jan16 comment $S$ is a subgroup of index $f$. Show that $fxS=S$ where $fx$ is $x^{f}$ and $fxS$ the left coset. Perfect! Understood! Thank you so much! My group theory from first semester is rusty. I completely forgot that given the ring structure requires an abelian additive group structure, all subgroups are normal and therefore allow for us to define quotient groups. Jan15 comment $S$ is a subgroup of index $f$. Show that $fxS=S$ where $fx$ is $x^{f}$ and $fxS$ the left coset. I'm having difficulty understanding the equalities you've presented. Would you mind clarifying please? Jan15 comment $S$ is a subgroup of index $f$. Show that $fxS=S$ where $fx$ is $x^{f}$ and $fxS$ the left coset. Hi, I am aware of that since the ring is not necessarily a group wrt multiplication. It only makes sense to define the cosets wrt addition. I still do not see why fx+S=S however. Jan15 asked $S$ is a subgroup of index $f$. Show that $fxS=S$ where $fx$ is $x^{f}$ and $fxS$ the left coset. Nov30 asked Given two fixed points on unit disk,find analytic functions from unit disk to unit disk that maximize the distance between values at the two points Nov28 comment Doesn't a function with constant modulus on the boundary of a bounded domain have constant modulus over the entire domain? Thank you! Thank you! Thank you! I really appreciate your help. Nov28 awarded Scholar Nov28 awarded Student Nov28 accepted Doesn't a function with constant modulus on the boundary of a bounded domain have constant modulus over the entire domain? Nov28 comment Doesn't a function with constant modulus on the boundary of a bounded domain have constant modulus over the entire domain? Thank you so much! Why is it required that the function be nowhere zero for the max/min modulus principle to apply? As well, I see that rotation is another such example, but I still do not see why the max/min mod principle does not apply here to imply a constant modulus over the disk. Nov28 asked Doesn't a function with constant modulus on the boundary of a bounded domain have constant modulus over the entire domain?