/Banach Space General/

Stop flooding /sci/ with these threads retard

What about sobolev spaces?

>>7773304
What's a Sobolev space?

>>7773306
They are Banach spaces.

>>7773296
And what do you want to discuss, your functional analysis homework?

>>7773306
Its used to solve nonlinear partial differential equations i think its cool

>>7773312
How can I begin functional analysis with only newb knowledge in analysis and linear algebra?

>>7773322
Read all three volumes of "Linear Operators" by Nelson Dunford and Jacob T. Schwartz

>>7773322
functional analysis is really my limit. I cannot do a single proof with C* algebras, I just can't.

>>7773304
They're subspaces of L^p spaces so I guess it's all right

>>7773328
where does one download these

>>7773306
Like
>>7773423
>>7773307
they are subspaces of L^p spaces, so they are Banach spaces that are separable (except for p=inf) and reflexive(except for p=1 and p=inf) and you can think of them of the spaces of L^p functions which are weakly differentiable, which is as the name suggests a generalisation of the usal derivative. Sobolev spaces are pretty much the core of modern theory of differential equations, which in fact is pretty much applied (nonlinear) functional analysis, where you can reduce the questions existence and uniqueness of a solution of a differential equation on properties of an operator between such a sobolev space and its dual space.

>>7773296
What about Frechet spaces?

>>7773447
internet