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Results tagged with ca.classical-analysis-and-odes
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user 152618
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
-2
votes
1
answer
167
views
Question about Lipschitz conditions
Let $f$ be a function on some real interval $[a,b]$. Suppose that $\forall x\in [a,b]$, there exists a positive constant $C$ such that
$$ |f(x)-f(y)| \leq C|x-y| $$
for all $y \in [a,b]$.
Does each $x …
- 419
6
votes
1
answer
459
views
A limit problem
Let $f$ be a bounded and continuous function, $0<a < 1$. $U(x,r)$ is the neighborhood of $x$ with diameter $r$. Can we prove the following equation of two limits
$$ \lim_{r\rightarrow 0} \sup_{y,z \i …
- 419
2
votes
1
answer
73
views
An inequality about the second-order difference
Fix a continuously differentiable but nowhere twice differentiable function $f$ on $\mathbb{R}$ supported on $[0,1]$. Is it true that for all $x\in[0,1]$ and all $\delta$ sufficiently small
\begin{ali …
- 419