All Questions
Tagged with applied-mathematics fa.functional-analysis
8 questions
8
votes
0
answers
686
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The function space defined by deep neural nets
Given a deep net graph and the activation functions on the hidden vertices do we have a description of the function space spanned by it? (even if for some specific architectures and activation ...
- 2,246
4
votes
2
answers
257
views
A functional inequality which calculates the limitation of human eyes
Find all pair of function $f^-,f^+:[0,1]\rightarrow[0,1]$ such that:
(1)$f^-(x)\leq x\leq f^+(x)$.
(2)$f^-(x)+f^+(1-x)=1$.
(3)$f^-(x)f^-(y)\leq f^-(xy)\leq f^-(x)f^+(y)$.
(4)$f^+(x)f^-(y)\leq f^+(xy)\...
- 1,462
3
votes
0
answers
115
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Linearized NLS/GP around a soliton and the spectrum of the evolution operator
I apologize if this has been asked before but so far I haven't found it anywhere.
Consider the Nonlinear Schrödinger equation with a potential (i.e. Gross- Pitaevskii) in $\mathbb{R}^{d}$
$$i\Psi_{t} =...
- 31
2
votes
1
answer
508
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What kind of role has Functional Analysis played in Signal Processing? [closed]
Does it serve mainly as a narration or is there any substantive consequence which might not be derived without tools of functional analysis?
- 29
2
votes
0
answers
70
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Multiexponential analysis of infection counts with errors
In the past, I have seen some decompositions of sums of exponential decays into components by the Padé-Laplace method: Apply the Laplace transform $${\frak L}(\sum_{i=1}^n a_i e^{k_i t}) = \sum_{i=1}^...
- 28k
1
vote
1
answer
354
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Mach's principle, Newton's law and Hilbert sphere?
(This question has originally been posted on reddit, but I thought, that the question raised in the post above, might fit as well here on MO.)
I wanted to share with you something I stumbled upon ...
- 3,064
1
vote
0
answers
85
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Maximizing the integral of a transformation that depends on a neighborhood of values of the original function
I'm not an expert in analysis whatsoever, so I might be posing a well-established question, or even an unanswerable one. Also, any suggestion on changes that might make the problem better are welcome.
...
- 11
1
vote
0
answers
114
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Spins in classical statistical mechanics
I'm reading Kupiainen's notes on the renormalization group and also caught my attention. Actually, this is something that often causes my some confusion. On page 43, in the section about Ginzburg-...
- 3,515