Question

Smooth curve confusion

score 72 · Answer 1 · 2023-03-17 21:39:01

72

Views

Smooth curve confusion

Published on 17 Mar 2023 - 21:39

score 42 · Answer 2 · 2023-03-25 21:30:44

42

Views

The function $\rho$ defined by $\rho (x) := \begin{cases} e^{1/ (|x|^2-1)} &\text{if } |x| <1 \\ 0 &\text{otherwise} \end{cases}$ is smooth

Published on 25 Mar 2023 - 21:30

score 50 · Answer 3 · 2023-03-25 22:00:44

50

Views

Brezis's Proposition 4.21: did the author mean $f \star \rho_n$ rather than $\rho_n \star f$?

Published on 25 Mar 2023 - 22:00

score 67 · Answer 4 · 2026-03-25 11:06:38

67

Views

$\mathcal C_c^\infty (\Omega)$ is dense in $L^\infty (\Omega)$ w.r.t. the weak topology $\sigma(L^\infty, L^1)$

Published on 25 Mar 2026 - 11:06

score 143 · Answer 5 · 2023-03-27 22:21:56

143

Views

Smooth monotonic function $f: [-1, 1] \to [-1, 1]$

Published on 27 Mar 2023 - 22:21

score 55 · Answer 6 · 2023-04-11 13:49:15

55

Views

Brezis' exercise 4.29: how to get rid of the dimension $d$?

Published on 11 Apr 2023 - 13:49

score 116 · Answer 7 · 2023-04-13 20:00:47

116

Views

Multiplication map on $SL(n, \mathbb{R})$ is $C^\infty$

Published on 13 Apr 2023 - 20:00

score 22 · Answer 8 · 2023-04-20 11:38:14

22

Views

If $f(w) = g(\langle w, x \rangle + y )$ with $g$ a $\beta$-smooth function. Show $f$ is $\left(\beta \|x\|^2\right)$-smooth

Published on 20 Apr 2023 - 11:38

score 27 · Answer 9 · 2023-05-02 08:54:01

27

Views

$C^k$-Norm of a Polynomial

Published on 02 May 2023 - 8:54

score 66 · Answer 10 · 2023-05-07 00:00:08

66

Views

Smooth interpolation between two sinusoidal functions, with constraints

Published on 07 May 2023 - 0:00

score 181 · Answer 11 · 2023-05-07 08:33:04

181

Views

$M$ is smooth compact manifold and $C_0,C_1$ disjoint closed subsets of $M$ so there is exists smooth func $f:M \to [0,1]$ s.t $f(C_0)={0},f(C_1)={1}$

Published on 07 May 2023 - 8:33

score 125 · Answer 12 · 2026-03-26 04:50:50

125

Views

Proving a certain map on $S^n$ is a diffeomorphism

Published on 26 Mar 2026 - 4:50

score 63 · Answer 13 · 2023-05-08 09:40:00

63

Views

Just how regular are the sample paths of 1D white noise smoothed with a Gaussian kernel?

Published on 08 May 2023 - 9:40

score 24 · Answer 14 · 2026-03-27 12:03:53

24

Views

Prove $\Gamma g_\varepsilon (0) = O( |\varepsilon |^k) $ as $ \varepsilon \to 0$, where $g$ is a smooth function, $\Gamma$ the difference operator

Published on 27 Mar 2026 - 12:03

score 84 · Answer 15 · 2026-03-25 20:11:56

84

Views

Are these smooth bump functions $\in C_{0}^{\infty}(-1,\ 1)$? $f(x) = \left(1+\exp\left(\frac{1-2|x|}{x^2-|x|}\right)\right)^{-1}$ and related

Published on 25 Mar 2026 - 20:11

List Question

Smooth curve confusion

The function $\rho$ defined by $\rho (x) := \begin{cases} e^{1/ (|x|^2-1)} &\text{if } |x| <1 \\ 0 &\text{otherwise} \end{cases}$ is smooth

Brezis's Proposition 4.21: did the author mean $f \star \rho_n$ rather than $\rho_n \star f$?

$\mathcal C_c^\infty (\Omega)$ is dense in $L^\infty (\Omega)$ w.r.t. the weak topology $\sigma(L^\infty, L^1)$

Smooth monotonic function $f: [-1, 1] \to [-1, 1]$

Brezis' exercise 4.29: how to get rid of the dimension $d$?

Multiplication map on $SL(n, \mathbb{R})$ is $C^\infty$

If $f(w) = g(\langle w, x \rangle + y )$ with $g$ a $\beta$-smooth function. Show $f$ is $\left(\beta \|x\|^2\right)$-smooth

$C^k$-Norm of a Polynomial

Smooth interpolation between two sinusoidal functions, with constraints

$M$ is smooth compact manifold and $C_0,C_1$ disjoint closed subsets of $M$ so there is exists smooth func $f:M \to [0,1]$ s.t $f(C_0)={0},f(C_1)={1}$

Proving a certain map on $S^n$ is a diffeomorphism

Just how regular are the sample paths of 1D white noise smoothed with a Gaussian kernel?

Prove $\Gamma g_\varepsilon (0) = O( |\varepsilon |^k) $ as $ \varepsilon \to 0$, where $g$ is a smooth function, $\Gamma$ the difference operator

Are these smooth bump functions $\in C_{0}^{\infty}(-1,\ 1)$? $f(x) = \left(1+\exp\left(\frac{1-2|x|}{x^2-|x|}\right)\right)^{-1}$ and related

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