Question

Does $\{\varphi(x)\in C_{c}^{\infty}(U)|\varphi(0)=0\}=\{x_{1}\psi_{1}+\cdots+x_{n}\psi_{n}|\psi_{i}\in C_{c}^{\infty}(U)\}?$

score 36 · Answer 1 · 2023-03-03 15:16:55

36

Views

Does $\{\varphi(x)\in C_{c}^{\infty}(U)|\varphi(0)=0\}=\{x_{1}\psi_{1}+\cdots+x_{n}\psi_{n}|\psi_{i}\in C_{c}^{\infty}(U)\}?$

Published on 03 Mar 2023 - 15:16

score 203 · Answer 2 · 2026-02-23 10:00:07

203

Views

Representation of an operator on a generalized eigenfunction

Published on 23 Feb 2026 - 10:00

score 77 · Answer 3 · 2026-03-26 13:42:21

77

Views

Find the fundamental solution in tempered distribution

Published on 26 Mar 2026 - 13:42

score 81 · Answer 4 · 2023-03-05 06:57:02

81

Views

Prove that different functions in $L^1_{\operatorname{loc}}(\Omega)$ define different distributions in $\mathcal D’(\Omega)$

Published on 05 Mar 2023 - 6:57

score 48 · Answer 5 · 2023-03-06 05:36:47

48

Views

Distributional Fourier transform of $F(x) = \log(-i(x+ia))$

Published on 06 Mar 2023 - 5:36

score 33 · Answer 6 · 2023-03-06 10:40:01

33

Views

Distribution (generalized function) takes non-negative value on non-negative function is of order 0

Published on 06 Mar 2023 - 10:40

score 38 · Answer 7 · 2023-03-08 08:50:41

38

Views

If the distributional derivative of a distribution is a funcion, is the original distribution a function too?

Published on 08 Mar 2023 - 8:50

score 211 · Answer 8 · 2023-03-10 07:54:45

211

Views

Does a distribution in the dual space of $C_0^\infty$ extend continuously to $C_b^\infty$?

Published on 10 Mar 2023 - 7:54

score 105 · Answer 9 · 2026-03-25 23:51:47

105

Views

PDEs: Derive source term of discontinuous advection equation (DGFEM)

Published on 25 Mar 2026 - 23:51

score 117 · Answer 10 · 2023-03-12 08:54:00

117

Views

Integral against a test function is bounded implies function is locally integrable

Published on 12 Mar 2023 - 8:54

score 95 · Answer 11 · 2023-03-12 22:28:42

95

Views

Existence of sequence of test functions converging to a constant

Published on 12 Mar 2023 - 22:28

score 52 · Answer 12 · 2023-03-14 19:01:23

52

Views

Infinite sum of positive semidefinite tempered distributions

Published on 14 Mar 2023 - 19:01

score 58 · Answer 13 · 2023-03-15 12:57:07

58

Views

Composition of function and delta function

Published on 15 Mar 2023 - 12:57

score 263 · Answer 14 · 2026-03-30 02:10:35

263

Views

Dirac delta distribution in the complex plane

Published on 30 Mar 2026 - 2:10

score 60 · Answer 15 · 2023-03-17 09:49:43

60

Views

Does any compact supported distribution restrictly depends on its support?

Published on 17 Mar 2023 - 9:49

List Question

Does $\{\varphi(x)\in C_{c}^{\infty}(U)|\varphi(0)=0\}=\{x_{1}\psi_{1}+\cdots+x_{n}\psi_{n}|\psi_{i}\in C_{c}^{\infty}(U)\}?$

Representation of an operator on a generalized eigenfunction

Find the fundamental solution in tempered distribution

Prove that different functions in $L^1_{\operatorname{loc}}(\Omega)$ define different distributions in $\mathcal D’(\Omega)$

Distributional Fourier transform of $F(x) = \log(-i(x+ia))$

Distribution (generalized function) takes non-negative value on non-negative function is of order 0

If the distributional derivative of a distribution is a funcion, is the original distribution a function too?

Does a distribution in the dual space of $C_0^\infty$ extend continuously to $C_b^\infty$?

PDEs: Derive source term of discontinuous advection equation (DGFEM)

Integral against a test function is bounded implies function is locally integrable

Existence of sequence of test functions converging to a constant

Infinite sum of positive semidefinite tempered distributions

Composition of function and delta function

Dirac delta distribution in the complex plane

Does any compact supported distribution restrictly depends on its support?

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