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Results tagged with real-analysis
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user 48609
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
0
votes
1
answer
140
views
growth of derivative
(Alexandre Eremenko gave the answer to the question I posted earlier. Then I realised the question didn't give what I wanted. Here is the updated question.)
Suppose that $f:[a,\infty)\to \mathbb{R}$ …
- 640
2
votes
0
answers
1k
views
bounds on derivatives of mollifiers/mollified functions
Consider the standard mollifier
$$
\phi(x) = C\exp\left(-\frac{1}{1-x^2}\right), \quad -1<x<1.
$$
such that $\int\phi(x) = 1$.
Let $f(x) = |x|$ and consider the convolution $f\ast \phi$. I am intere …
- 640
1
vote
1
answer
164
views
mollifier satisfying moment conditions
I wish to find a mollifier $\psi\in C_0^{d+1}(-1,1)$ such that
$$
\int_{-1}^1 x^k \psi(x)dx = \begin{cases}
1, & k=0;\\
0, & k=1,\dots,d.
\end{cases}
$$
This paper (https://home.cscamm.umd.edu …
- 640