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Results tagged with growth-rate
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user 409412
2
votes
1
answer
202
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Geometry in Hilbert spaces / spheres in high dimensions
Let $H$ be a separable Hilbert space of infinite dimension and let $(e_n)_{n \in \mathbb{N}}$ be an orthonormal basis of $H$. For a series $(\alpha_n)_{n \in \mathbb{N}} \subset \mathbb{R^+}$ we are i …
- 1,295
1
vote
0
answers
50
views
When are ellipsoids in a convex hull of a sequence with prescribed growth rate?
I am currently reading Dudley's 'Uniform Central Limit Theorems' and found two sections which together would have an interesting geometric interpretation for ellipses in Hilbert spaces. I would like t …
- 1,295
0
votes
0
answers
124
views
A weaker condition on Fourier coefficients for boundedness of the function
Let $f : \mathbb{S}_1 \rightarrow \mathbb{C}$ be a square-integrable fnction and let $(\widehat{f}_k)_{k \in \mathbb{Z}}$ be its Fourier-coefficients. It is very well known, that the condition $\sum\l …
- 1,295