Okay, now that I'm looking at it, its more than obvious. The red flag that got me was that it mentioned the word sequence and I didn't really get that because I always viewed this as a series not a sequence, as if they were different.
But as you have shown me, while you are calculating the...
In my book, applied analysis by john hunter it gives me a strange way of stating an infinite sum that I'm still trying to understand because in my calculus books it was never described this way.
It says:
We can use the definition of the convergence of a sequence to define the sum of an...
^ I don't think using cauchy sequences does the job here. my teacher said I want to show closed. i don't see how cauchy shows how these spaces are closed.
Thanks.
I think I now have the answer to part 1 because you can use an idea from Parseval which automically shows that en weakly converges to zero. But I'm still not sure about what to do with an and un. I also think the boundedness of an plays a role.
For part 2 I know that this is showing...
Homework Statement
This is a problem from Haim Brezis's functional analysis book.
Homework EquationsThe Attempt at a Solution
I'm assuming (e)n is the vectors like (e)1 = (1,0,0), (e)2=(0,1,0) and so on.
We know every hilbert space has an orthonormal basis.
I also need to know the...
Homework Statement
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Let M, N be a subset of a Hilbert space and be two closed linear subspaces. Assume that (u,v)=0, for all u in M and v in N. Prove that M+N is closed.
Homework Equations
I believe that (u,v)=0 is an inner product space
The Attempt at a Solution
This is a problem from...
Okay, so this problem was the example problem in my engineering math book. I tried to do the example before getting to the actual problems. Now I tried the same technique on the first problem and I checked out my solution to see if it worked and it only half worked.
The problem I'm having is...
Thank you so much! I solved the equation.
x(t)=c1t+c2tln(t)+t[ln(t)]^2
the matrix solution seems to be the wronstkian of the functions next to the c1 and c2, however the third term which doesn't have a constant I'm not sure what to do with it or if it has any significant importance.
Homework Statement
Find general solution of the given problem in the picHomework Equations
All I need to know is where they found the fundamental set of solutions.
The Attempt at a Solution
All I need to know is where they found the fundamental set of solutions. Please see pic. All I want...
Okay I'm still trying to master this topic. Can someone please explain to me how they got linear dependent on this following problem.
u = (e^t,0)
v = (0,0)
w = (0, e^t)
How is this dependent? I cannot for the life of me find something like au + bv = w.
actually i don't think that is so.
t-t^2 is not a -2 multiple of -2t+4t^2
the 4 makes it not work like this.
Also on number 5 in my homework I have this problem:
u = ( 2-t,t,-2) v = (t, -1, 2 ) w = (2+t, t-2, 2 )
it says in the answer is linear dependent, yet how can this be? I do not...