Question

Is the Laplacian of any test function in $C_0^\infty$ still a test function?

score 91 · Answer 1 · 2026-04-10 17:56:25

91

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Is the Laplacian of any test function in $C_0^\infty$ still a test function?

Published on 10 Apr 2026 - 17:56

score 44 · Answer 2 · 2026-04-16 05:21:05

44

Views

If a distribution $f$ 's all $k$ order weak derivatives are zero on $\mathbb R^n$,Then $f$ must be the polynomal with at most $k-1$ order?

Published on 16 Apr 2026 - 5:21

score 134 · Answer 3 · 2026-04-11 23:38:26

134

Views

Confusions when differentiating a Fourier Transform and using the Kramers-Kronig relations

Published on 11 Apr 2026 - 23:38

score 123 · Answer 4 · 2026-04-16 01:10:35

Proof of $z^{-1 + \epsilon} = \frac{1}{\epsilon} \delta(z) + \sum_{k = 0}^\infty \frac{\epsilon^k}{k!} \left( \frac{\ln z}{z} \right)_+$

score 107 · Answer 5 · 2026-04-13 20:15:08

107

Views

Is there a smooth tempered distribution $u$ such that $\sum_{j=0}^\infty 2^{-j} u(x-j)$ is not smooth?

Published on 13 Apr 2026 - 20:15

score 293 · Answer 6 · 2026-04-11 15:00:23

293

Views

Dual of space of compactly supported distribution is space of smooth functions.

Published on 11 Apr 2026 - 15:00

score 41 · Answer 7 · 2026-04-11 22:39:45

41

Views

Calculation of attainment level based on average

Published on 11 Apr 2026 - 22:39

score 56 · Answer 8 · 2026-04-13 20:30:45

56

Views

Manifold re-expressed as a generalized distribution function.

Published on 13 Apr 2026 - 20:30

score 40 · Answer 9 · 2026-04-14 21:48:31

40

Views

Fitting distribution to histogram (the only data)

Published on 14 Apr 2026 - 21:48

score 58 · Answer 10 · 2026-04-16 16:44:53

58

Views

Why is this limit true in the distribution sense?

Published on 16 Apr 2026 - 16:44

score 26 · Answer 11 · 2026-04-13 08:15:38

26

Views

Is the convolution operator with kernel $(1+|x|^2)^\frac{n}{2}$ bounded between Lebesgue spaces?

Published on 13 Apr 2026 - 8:15

score 48 · Answer 12 · 2026-04-13 02:10:45

48

Views

The dual space of one special subspace of $C^{\infty}_0$

Published on 13 Apr 2026 - 2:10

score 377 · Answer 13 · 2026-04-13 17:17:55

377

Views

Integral of Dirac[t] delta function

Published on 13 Apr 2026 - 17:17

score 93 · Answer 14 · 2026-04-12 18:56:43

93

Views

Is my derivation of the derivative of a product of the Heaviside function and a function correct? (A follow-up question)

Published on 12 Apr 2026 - 18:56

score 81 · Answer 15 · 2026-04-11 12:43:48

81

Views

Question about the Dirac Delta

Published on 11 Apr 2026 - 12:43

List Question

Is the Laplacian of any test function in $C_0^\infty$ still a test function?

If a distribution $f$ 's all $k$ order weak derivatives are zero on $\mathbb R^n$,Then $f$ must be the polynomal with at most $k-1$ order?

Confusions when differentiating a Fourier Transform and using the Kramers-Kronig relations

Proof of $z^{-1 + \epsilon} = \frac{1}{\epsilon} \delta(z) + \sum_{k = 0}^\infty \frac{\epsilon^k}{k!} \left( \frac{\ln z}{z} \right)_+$

Is there a smooth tempered distribution $u$ such that $\sum_{j=0}^\infty 2^{-j} u(x-j)$ is not smooth?

Dual of space of compactly supported distribution is space of smooth functions.

Calculation of attainment level based on average

Manifold re-expressed as a generalized distribution function.

Fitting distribution to histogram (the only data)

Why is this limit true in the distribution sense?

Is the convolution operator with kernel $(1+|x|^2)^\frac{n}{2}$ bounded between Lebesgue spaces?

The dual space of one special subspace of $C^{\infty}_0$

Integral of Dirac[t] delta function

Is my derivation of the derivative of a product of the Heaviside function and a function correct? (A follow-up question)

Question about the Dirac Delta

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