Recent content by hooker27

Hi, I need your help with a very standard proof, I'll be happy if you give me some detailed outline - the necessary steps I must follow with some extra clues so that I'm not lost the moment I start - and I'll hopefully finish it myself. I am disappointed that I can't proof this all by myself...

Sorry for the duplicate.

Let f(t) be a function in L^2. I am interested under which conditions converges the integral \int_0^\infty \frac{|F(\omega)|^2}{\omega} d\omega where F(omega) denotes the Fourier transform of f. My book, well, several books actually, say the sufficient conditions are 1) F(0) = 0...

Thanks to you both, I think I do understand the difference now. As for the observations, the proofs could be as follows: 1) Since X is Banach, a given Cauchy sequence in E (which must then also be in X) converges to a point in X and since E is closed, every sequence from E that converges in X...

No, it is not. While studying some proofs I relized that I know two different definitions for the two different things but I can't really put my finger on the differences, if there are any. But I do not see the purpose of your question, except that you would 'educate' me that I posted in a...

Hi to all What exactly is the difference between Banach(=complete, as far as I understand) (sub)space and closed (sub)space. Is there a normed vector space that is complete but not closed or normed vectore space that is closed but not complete? Thanks in advance for explanation and/or examples.

Won't work for n=2: Let G_1 and G_2 be blonde girls and le't assume the theorem is true for n=1. If, for example G_1 is blonde, we can't take G_2 to the collection with her (that would be n=2), so we can't prove that G_2 is also blonde. Hence the induction stops at n=1 and you'll never reach...

- I am not sure which 'i' (and 'typo') you are referring to, your 'indentity' is, as far as I can say, identical to mine. - So make this clear for me: when can I use the fact that (A*B)^x = A^x*B^x when A,B are complex and x real? (I have little knowledge of complex analysis) I need to get...

Hi Where is the error is this 'identity'?: (-e^i)^{\frac{1}{2}} = (-1)^{\frac{1}{2}}*e^{\frac{i}{2}} My calculator says that the right side is minus one times the left but I can't see the mistake I'v made. Help me please, thanks.

Maybe there is s different name for that in english. What I know as Newton's integral is this: if a function f is defined on (a,b) and there exists some F such that F'(x) = f(x) for all x from (a,b) (in other words - the function F is an antiderivative of f on (a,b) ) then Newton's integral of...

This question arised in my last math class: If a sequence of functions f_n uniformly converges to some f on (a, b) (bounded) and all f_n are integrable on (a, b), does this imply that f is also integrable on (a, b) ?? (f_n do not necessarily have to be continous, if they were, the answer...

Ok, I'll calm it down but tell me what you think about this: You are right that 0=0a is true for all a but 0/0=a is nonsense since 0/0 is not assigned any value, you can't divide by 0. But I don't want to argue over something so simple, let's look at this: If you say, that 1/0 does not...

I believe that the limit indeed does not exist, one must be careful with multivariable limits, even with the most obvious limits. For example \lim_{x \rightarrow 0} \frac{x}{x} = 1 but \lim_{\substack{x \rightarrow 0 \\ y \rightarrow 0}} \frac{x}{x} does not exist, for the same reasons I...

Maybe I got it wrong but it looks to me that the limit \lim_{\substack{x \rightarrow 0 \\ y \rightarrow 0}} \frac{x + y}{\sin x + \sin y} clearly does not exist, is that your result? When approaching the (0,0) point from y=-x direction, the function is 0/0 and thus undefined (not...