set of course, not basis...thank you
but it doesn't work:
\sum_{k=1}^\infty |<x,x_k>|^2 =|<x,x_1>|^2=|\frac{2}{\sqrt(2)}|^2=2,
or am I just really bad at simple calculations today?
Hi everyone
Today during problem session we had this seemingly simple exercise, but I just can't crack it:
We should give an example of an x \in \ell^2 with strict inequality in the Bessel inequality (that is an x for which \sum_{k=1}^\infty |<x,x_k>|^2 < ||x||^2, where (x_k) is an orthonormal...
when it comes to limits I like to have some theorem to backup intuition. but okay, this time it really is obvious as you say, so I'll just accept it :)
thanks for the reply.
The problem as I see it is that you cannot look at the limit of the numerator and denominator separately, so to me it seems like these arguments doesn't work. But I think i have figured it out:
If you do the following...
Hi
I just found an old high school math exercise and was wondering how it should be answered mathematically correct. The exercise is:
Given lim f(x)=(x^2+x+a)/(x-1) = 3 for x->1, determine a. Back in high school I used to say something like this:
Since the denominator goes to 0 for x ->...
okay, think I found out why it doesn't work.
The derivative of a function is not equal to the derivative of the function's Fourier Series in general. So obviously my method won't work.
example:
http://www.advancedphysics.org/forum/showthread.php?t=7278"
Hello
I have been wondering for some time about, why I have to use orthogonality properties in a special kind of PDE problem I have encountered a few times now.
As an example see exercise 13-3 in this file:
http://www.student.dtu.dk/~s072258/01246-2009-week13.pdf"
I have described my...