Thanks, linearly independent is exactly what it meant :)
So it's a sequence of linearly independent vectors that span the entire space. It makes sense
because the author states that this sequence is not necessarily orthonormal.
Hi!
I'm reading a book on the finite element method and the author mentions a free and total sequence in a hilbert space. I've been searching the internet, but I just can't find the definition of a free sequence. Does anybody know what it is?
Thanks in advance
To make things clearer, consider this example(I think this is the function g_edgar mentioned).
Let \psi(x) be a smooth non-negative function such that its support is contained in the interval (-1,1) and such that \int_R\psi(x)dx=1.
Now consider the series \sum_{k=1}^\infty k\psi ((x...
Thanks for the quick answers. With smooth I just meant that all the derivatives exist and are continuous. So with smooth I meant to disallow for the above mentioned example regarding sets of measure zero.
And yes, the question was about one single function, but I think the sequence of bumps...
smooth and L^2 on R^n. Will it be bounded??
Hello,
If a function, say u, is smooth and L^2 on R^n. Will it be bounded??
In the case of n=1 I would say that it obviously is so. Because if it were unbounded then it wouldn't be L^2.
But in the case of n=2 (or higher). I can imagine a...