List questions from smooth-functions

Published on 19 May 2023 - 5:35

120

Views

How to show that the function $r \mapsto\ln u(e^r)$ is convex when $u$ is an absolutely monotonic function?

Published on 21 May 2023 - 5:39

119

Views

Problem about the construction of a smooth function

Published on 21 May 2023 - 11:35

67

Views

Is it possible to represent any C-infinite function as some Maclaurin/Taylor series?

Published on 25 May 2023 - 9:42

52

Views

On embeddings of $\mathbb{R}^n$ with the same image

Published on 25 May 2023 - 20:18

58

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Do smooth bijections always preserve Hausdorff dimension?

Published on 26 Mar 2026 - 1:17

64

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Milnor's definition of smooth functions on manifolds as subsets of $\mathbb{R}^k$

Published on 29 May 2023 - 11:01

259

Views

Question about the "nowhere analyticity" of the Fabius function

Published on 26 Mar 2026 - 6:32

97

Views

Under which condition $d(y)=\min_x f(x,y)$ is smooth ($C^1$) (similar to Danskin's theorem))?

Published on 06 Jun 2023 - 19:21

96

Views

On the solution to $u'(x)=2u(2x+1)-2u(2x-1)$ and the Fabius function

Published on 25 Mar 2026 - 20:11

63

Views

Diffeomorphisms of $(-1,1)^n$ sending fixed point to origin

Published on 26 Mar 2026 - 3:11

326

Views

Checking if functions are well defined Mollifiers kernels (Test functions / Bump functions)

Published on 26 Mar 2026 - 15:16

116

Views

Approximating homeomorphisms by diffeomorphisms on manifolds

Published on 19 Jun 2023 - 20:35

67

Views

Function not being continuous, but being $C^{\infty}$ in Tu's book

Published on 26 Jun 2023 - 10:59

48

Views

Smoothness of quotient of multivariable smooth function by degree 1 polynomial

Published on 28 Jun 2023 - 20:24

List Question

$f:M\to N$ is smooth iff $\forall g\in C^\infty(N)$, $g\circ f\in C^\infty(M)$

How to show that the function $r \mapsto\ln u(e^r)$ is convex when $u$ is an absolutely monotonic function?

Problem about the construction of a smooth function

Is it possible to represent any C-infinite function as some Maclaurin/Taylor series?

On embeddings of $\mathbb{R}^n$ with the same image

Do smooth bijections always preserve Hausdorff dimension?

Milnor's definition of smooth functions on manifolds as subsets of $\mathbb{R}^k$

Question about the "nowhere analyticity" of the Fabius function

Under which condition $d(y)=\min_x f(x,y)$ is smooth ($C^1$) (similar to Danskin's theorem))?

On the solution to $u'(x)=2u(2x+1)-2u(2x-1)$ and the Fabius function

Diffeomorphisms of $(-1,1)^n$ sending fixed point to origin

Checking if functions are well defined Mollifiers kernels (Test functions / Bump functions)

Approximating homeomorphisms by diffeomorphisms on manifolds

Function not being continuous, but being $C^{\infty}$ in Tu's book

Smoothness of quotient of multivariable smooth function by degree 1 polynomial

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