Recent content by arthurhenry

The following comes from the complex analysis text by Joseph Bak: He is trying to determine all conformal mappings f of upper half plane H onto the unit disk. "Let us first assume that f is an LFT and f(a)=0 for Im(a)>0. Then, since the real axis is mapped into the unit circle, it...

Thank you, this is a very good hint.Having said that this is where I am: Each point p in unit disk D is mapped to a point. But (following your hint), f(p) is not assumen unless it is real, so f maps all of D to reals. Therefore, by Open Mapping Theorem, since the image has no interior points...

There does not exist a non-constant analytic function in the unit circle which is real valued on the unit circle. I am not able to see why. I am trying to apply Louisville's Theorem, or maybe Open Mapping Th., but I fail. Is there a way of extending this function so that it entire? and even...

Thank you, that has cleared things very nicely for me.

I think I understand it now. I think you are saying: suppose p is a point inside the disk, i.e. an interior point. Take nbhd around p that is contained in the unit disk still. Then by Open Mapping Theorem, the image of this disk is open, i.e., the f(p) is also contained in a nbhd that is also...

In the text by Joseph Bak, He is trying to determine all automorphisms of the unit disk such that f(a)=0. He says "let us suppose that this automorphism is a linear fractional transformation. Then it must map the unit circle onto the unit circle. I am asking for help in understanding this...

Somewhat embarrassing... Thank you very much for the help

I was thinking: if f' were to be never zero, then how can Integral[f'/f] around a circle be zero. The integral should be zero as f has no zeros inside the circle...Is what I am thinking. Than you for your time again

Two questions: 1)Quote comes from a textbook: Each non-constant function analythic function with f(0)=0 is,in a small nbhd of 0, the composition of a conformal map with the nth-power map...The proof is given and I think I am comfortable with it.. My question is a lot simpler (I think)...

The context is polytopes...reading some introductory material. It talks about two points in R3, namely p=(1,0,0) and q=(0,1,0) and tells me to notice that the linear span of of p and q and the affine span of p and q are not the same. Could somebody tell me the difference? Thanks

I am reading this reply by you only now Micromass, thank you. For some reason (mostly because it appears as a problem on a final exam), I assumed it would have some other, perhaps easier, solution. It seems like once 144 is determined, one calculates this by brute force. Yes, most of my...

Yes, I did try, and at the time I though I solved it. My problem has been after "reducing the problem to a Jordan block"... Thank you

Why is every matrix (complex) similar to its transpose? I am looking at a typical jordan block and I see that the transpose of the nilpotent part is again nilpotent and actually similar to the nilpotent part. I can see that the scalar part of the jordan block does not change under...

Okay, perhaps I rushed in saying that I see why Q is not a free Z-Module. I am not able to see it. I am also not seeing how I can apply Fund. Theroem. of Fin. Gen. Abelian groups. Are you suggesting Micromass that "use it to get a contadiction"...I guess I am not sure if I see what is fin...

There is yet another comment on http://planetmath.org/encyclopedia/RankOfAModule.html which says that two different basis sets for an R-Module may have different cardinality. This one I cannot produce an example for (I am trying two finite cases for example)