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Results tagged with fa.functional-analysis
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user 43954
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
An infinite set in a compact space
It seems the following.
Dealing with continuous functions on a topological space $X$, it is natural to consider $X$ to be Tychonoff, or, at least, functionally Hausdorff. I recall that a space $X$ i …
- 5,409
3
votes
Mutual metric projection
I started to investigate properties of possible required map $S$, but they are hard to grasp,
so my vision of them is very coarse, see the propositions below.
But I shall try to use them to refine des …
- 5,409
2
votes
Polynomial $f(x)$ has positive coefficients and only real roots. How many polynomials formed...
I provide my answer to Mathematics.SE cross-post
of the question to inform MathOverflow community.
Some results from this answer are already in Blue's answer
to the cross-post. Following it, we shall …
- 5,409
4
votes
0
answers
2k
views
Approximation of continuous functions by Lipschitz functions in the topology of uniform conv...
I was involved into this subject when I answered
this
question from MSE. Trying to generalize my answer, I am thinking about a following
Question. Let $X$ and $Y$ be metric spaces. When each continuo …
- 5,409
6
votes
If the Hausforff dimension of the graph of a function $u$ is $N$ and $\tilde u = u$ a.e. the...
Put $N=1$, $M=2$, $\Omega=\Bbb R^N$, and $u(x)=(x,0)$ for each $x\in\Bbb R^N$. Then the graph of $u$ is a straight line, so it has Hausdorff dimension $1=N$. On the other hand, let $C\subset [0,1]$ be …
- 5,409