Recent content by stradlater

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.

Yes, it's the book Numerical Analysis by Roger Temam. Translated from french.

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...