Question

Understanding a proof why $\lim_{\epsilon\downarrow 0}\frac{1}{\epsilon\sqrt{2\pi}}e^{\frac{-x^2}{2\epsilon^2}} = \delta(x)$

score 200 · Answer 1 · 2026-04-15 20:00:26

200

Views

Understanding a proof why $\lim_{\epsilon\downarrow 0}\frac{1}{\epsilon\sqrt{2\pi}}e^{\frac{-x^2}{2\epsilon^2}} = \delta(x)$

Published on 15 Apr 2026 - 20:00

score 49 · Answer 2 · 2026-04-11 06:08:23

49

Views

How to prove the Leibniz's rule for the product of a function and a generalized function ?.

Published on 11 Apr 2026 - 6:08

score 43 · Answer 3 · 2026-04-12 20:43:54

43

Views

on a family of inner products generating the usual Schwartz topology

Published on 12 Apr 2026 - 20:43

score 214 · Answer 4 · 2026-04-12 17:36:55

214

Views

If the distributional derivatives are locally in $L^2$, can we conclude that the function is locally in $L^2$

Published on 12 Apr 2026 - 17:36

score 47 · Answer 5 · 2026-04-15 08:04:30

47

Views

Distribution supported on a cross

Published on 15 Apr 2026 - 8:04

score 221 · Answer 6 · 2026-04-12 01:58:07

221

Views

Why does Dirac's delta distribution have an infinite energy?

Published on 12 Apr 2026 - 1:58

score 62 · Answer 7 · 2026-04-10 14:30:05

62

Views

A direct computation on Dirac delta function

Published on 10 Apr 2026 - 14:30

score 43 · Answer 8 · 2026-04-14 20:08:58

43

Views

Product of Delta distributions of a submanifold

Published on 14 Apr 2026 - 20:08

score 38 · Answer 9 · 2026-04-17 04:23:45

38

Views

Commutator with x vs commutator with smooth function

Published on 17 Apr 2026 - 4:23

score 71 · Answer 10 · 2026-04-12 16:08:22

71

Views

Jensen's for continuous convex combinations

Published on 12 Apr 2026 - 16:08

score 80 · Answer 11 · 2026-04-13 08:05:07

80

Views

Product Rule and Distributions

Published on 13 Apr 2026 - 8:05

score 51 · Answer 12 · 2026-04-14 11:49:20

51

Views

Probability generating function for $\mathbb{N}\cup\left\{\infty\right\}$

Published on 14 Apr 2026 - 11:49

score 83 · Answer 13 · 2026-04-16 20:20:12

83

Views

Why $T: L^1_{\text{loc}}(G) \to C_0^\infty(G)^*$ is an injection?

Published on 16 Apr 2026 - 20:20

score 64 · Answer 14 · 2026-04-10 19:36:34

64

Views

Confusion regarding terminology in Distribution theory and Calderon-Zygmund Theorem.

Published on 10 Apr 2026 - 19:36

score 36 · Answer 15 · 2026-04-15 21:11:00

36

Views

Under which integrability condition is the convolution with a Dirac comb well-defined?

Published on 15 Apr 2026 - 21:11

List Question

Understanding a proof why $\lim_{\epsilon\downarrow 0}\frac{1}{\epsilon\sqrt{2\pi}}e^{\frac{-x^2}{2\epsilon^2}} = \delta(x)$

How to prove the Leibniz's rule for the product of a function and a generalized function ?.

on a family of inner products generating the usual Schwartz topology

If the distributional derivatives are locally in $L^2$, can we conclude that the function is locally in $L^2$

Distribution supported on a cross

Why does Dirac's delta distribution have an infinite energy?

A direct computation on Dirac delta function

Product of Delta distributions of a submanifold

Commutator with x vs commutator with smooth function

Jensen's for continuous convex combinations

Product Rule and Distributions

Probability generating function for $\mathbb{N}\cup\left\{\infty\right\}$

Why $T: L^1_{\text{loc}}(G) \to C_0^\infty(G)^*$ is an injection?

Confusion regarding terminology in Distribution theory and Calderon-Zygmund Theorem.

Under which integrability condition is the convolution with a Dirac comb well-defined?

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