Recent content by esisk

I apologize that I am posting this in this section, but... I wish that people did not reply to a thread and then merely state what they_do not know_ about the subject and what their experinece has been in life regarding the subject matter... Unfortunately,as a consequence, seeing that a...

Can somebody give me an example whereby I use the inversion with respect to a circle (unit circle or otherwise) and the problem becomes easier. I guess I am asking: how do I make use of this notion. Or a problem that involves inversion, period. Thank you

Hope this does not sound vague! 1) I a looking at the Poisson's formula for the disk. Can somebody give me an example how one uses this, or a question where we use it to solve the problem. What is it exactly saying that Cauchy's formula is not saying? Thank you 2) Can somebody give me an...

Thank you for the response Hawkeye... I am testing my understanding of your hints: First we suppose that f were analythic in the interior of the circle ,say r=2. Then the integral around the unit circle would be zero (by Cauchy), Whereas...,if f=1/z on the unit circle, then f=1/z on a...

Hi, Is there a function holomorphic on the open unit disk and continuoes on the closed disk such that f(z)= 1/z on the unit circle? I will also like to know if somebody can help: There are several approximation theorems out there, say Mergelyan, Runge, etc. Can somebody point at the...

How do I integrate sin(x^2) please? Not (sin(x))^2. Thanks again

Thank you, I will try to get a hold of it.

Hi All, I am trying to learn about Linear Algebraic Groups. I am using the book by James Humpreys. I love the subject, but I find it a bit, say, not so beginner-friendly. My goal is not being spoon-fed, but I am very interested in finding a source(s) whereby one is able to go through some...

Thank you Eynstone. I am sure it all is there, but I am just trying to digest it in my own pace now.

I thank you very much Eynstone. Need to study more...I am not prelim-ready yet Regards

I thank you very much Eynstone. Need to study more...I am not prelim-ready yet Regards

Hello All, Just when I thought I understood whatever there was to understand about Normal Families... F(z) is analytic on the punctured disk and we define the sequence f_{n}=f(z/n) for n \leq 1. Trying (and failing) to show that {f_n} is a normal family on the punctured disk iff the...

I thank you edgar, I think I see it now. So I suspect we get the full symmetric group on n letters then, as the automorphism group. Thank you again

how do we describe the biholomorphic self maps of the multiply puncture plane onto itself? I mean C\{pi,p2,p3..pn} Plane with n points taken away. I wanted to generailze the result for the conformal self maps of the punctured plane, but I do feel these are quite different animals. I...

Thank you both of you. I retrospect, I should have made it clearer by saying the open disk. And, yes, following the suggestion from Edgar I can use (z-i)^2 to map the upper falf plane onto C and Cayley map to map the open disk onto the upper half plane. I believe this will do it. Thsnk...