0
votes
2answers
61 views

Important applications of the Uniform Boundedness Principle

There's like three applications of the uniform boundedness principle in wikipedia: 1) If a sequence of bounded operators converges pointwise to an operator, then the limit operator is also bounded, ...
0
votes
1answer
242 views

Functional Analysis - Where to go from here?

The short version of this question is this: I like functional analysis and want to learn more. I've taken a class on it and I've read the books by Brezis and Conway. Where can I go from here? Do ...
11
votes
3answers
931 views

problem books in functional analysis

There are many excellent problem books in real analysis.I'm looking for a problem book in functional analysis or a book which contains a lot of problems in functional analysis (Easy and hard problems) ...
6
votes
2answers
269 views

Paley-Wiener type theorems for distributions?

In general a theorem of Paley-Wiener type gives a relation between the decay of a function and the smoothness of its Fourier transformation, and there are plenty of them since there are many kinds of ...
68
votes
18answers
7k views

Your favourite application of the Baire Category Theorem

I think I remember reading somewhere that the Baire Category Theorem is supposedly quite powerful. Whether that is true or not, it's my favourite theorem (so far) and I'd love to see some applications ...
32
votes
3answers
827 views

Instructive proofs in functional analysis

I am beginning to learn functional analysis (from Folland and Royden), but I am from a non-mathematical background, so I often encounter techniques in proofs that I am not familiar with (for example ...
35
votes
3answers
2k views

What is the spectral theorem for compact self-adjoint operators on a Hilbert space actually for?

Please excuse the naive question. I have had two classes now in which this theorem was taught and proven, but I have only ever seen a single (indirect?) application involving the quantum harmonic ...
3
votes
3answers
142 views

Explicit examples of functions with flow?

Let's say that $f(x)=f^{1}(x)$ and that $f(f(x))=f^{2}(x)$. Moreover, $f^{n}(x)$ is the n-th iterate of $f(x)$, for $n \in \mathbb{N}$. I'm curious about extending iteration to larger number sets. For ...