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/sci/ - Science & Math

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15095243 No.15095243 [Reply] [Original]

what's functional analysis all about. What are the most important theorems. Is it fun?

>> No.15095244

Do you expect us to copy the Wikipedia article or what?

>> No.15095249

>>15095244
>us
I expect you and your gay bf stay out of my thread, when you're not interested in the topic.

>> No.15095392

i find reproducing kernel hilbert spaces to be very useful in my applications

>> No.15095405

>>15095392
what are these applications?

>> No.15095418

>>15095405
machine learning

>> No.15095420

How about you just buy a book about functional analysis? I bet dover has some reprint for 10 bucks going on. Read it and find out yourself

>> No.15095439

>>15095420
I'm currently learning about functional analysis in the context of real analysis. I've been studying equicontinuity, pointwise and uniform convergence, the Arzela-Ascoli theorm and some basic fixed-point theorems, the ones from Banach and Brouwer.
I made this thread in order to find out how this all relates to functional analysis and its core concepts. I'm also interested in how people perceive it: What's interesting about it, its applications etc.

>> No.15095440

Functional analysis is linear algebra for infinite dimensional systems: infinite dimensional systems of equations or the matric algebra of infinite dimensional matrices. It is important for QFT. An important theorem probably states the existence of the functional derivative.