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Results tagged with fa.functional-analysis
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user 69029
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
4
votes
1
answer
168
views
Bounding $\int_{\mathbb{R}_{+}}W(x,\lambda)W(y,\lambda)d\lambda$
Let $$W:\mathbb{R}_{+}^{2}\rightarrow(0,1]$$ be a symmetric, integrable function. Let $$f(x)=\int_{\mathbb{R}_{+}}W(x,\lambda)d\lambda$$ and assume this function is monotonically non-increasing. Is th …
2
votes
0
answers
98
views
What does integrability of a strictly monotonic function imply about the tails of that funct...
In particular, if $f:\mathbb{R}_{+}\rightarrow[0,1]$ is a strictly monotonic decreasing function and $f$ is integrable then does it necessarily hold that $f^{-1}(1/t)=o(t)$?