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Results tagged with real-analysis
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user 50777
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
3
votes
The relation between the convergence of the infinite integral of xf' and f
Since $f$ is monotically decreasing to $f(+\infty) = 0$, $f$ is nonnegative. Hence, to prove that $\int_a^{+\infty} f$ converges, it is sufficient to prove that, $\int_a^b f$ is uniformly bounded abov …
- 981
2
votes
0
answers
88
views
A division of real analytic functions
Problem statement
Let $f,g \in C^\omega(X,\mathbb{R})$ be two real analytic functions over a real Banach space $X$.
Assume that, for every $n \in \mathbb{N}$, there exists $C_n>0$ and $h_n \in C^\omeg …
- 981
1
vote
Accepted
Constrained linear optimization problem on $C^1$
As you suggest, let me consider the case $f \equiv 1$. Without loss of generality, assume also that $a = 0$ and $b = 1$. Let $\sigma := o(1)/o(0) \in (0,1)$. The problem becomes
$$
\sup_{v \in C^1([0, …
- 981