Question

Prove the independence of "a" of a Fourier coefficient of a Fourier series calculated over the interval $[-a,a]$

score 27 · Answer 1 · 2026-04-13 21:37:09

27

Views

Prove the independence of "a" of a Fourier coefficient of a Fourier series calculated over the interval $[-a,a]$

Published on 13 Apr 2026 - 21:37

score 45 · Answer 2 · 2026-04-14 00:44:36

45

Views

computing $L^p-$norm of nice function.

Published on 14 Apr 2026 - 0:44

score 30 · Answer 3 · 2026-04-16 18:45:21

30

Views

Positivity of the Fourier transform: prove or disprove that $\operatorname{Re}(\overline{\widehat{u}}(\xi) \widehat{F\circ u}(\xi))\geq0$

Published on 16 Apr 2026 - 18:45

score 68 · Answer 4 · 2026-04-11 20:23:41

68

Views

Inequality regarding a function and its Fourier transform

Published on 11 Apr 2026 - 20:23

score 48 · Answer 5 · 2026-04-16 02:23:43

48

Views

If $1/m$ is a Fourier multiplier in $L^p,$ then is $1/(1+m)$ also a Fourier multiplier?

Published on 16 Apr 2026 - 2:23

score 46 · Answer 6 · 2026-04-15 14:40:21

46

Views

Any constant function is a Fourier Multiplier in $L^p(\mathbb{R}^n)$?

Published on 15 Apr 2026 - 14:40

score 118 · Answer 7 · 2026-04-11 18:08:17

118

Views

Relation between FT of function and FT of modulus squared function

Published on 11 Apr 2026 - 18:08

score 71 · Answer 8 · 2026-04-16 05:54:29

71

Views

When is a solution $P(f'(x)) = Q(f(x))$ periodic or double periodic?

Published on 16 Apr 2026 - 5:54

score 184 · Answer 9 · 2026-04-09 17:37:41

184

Views

How does the multidimensional Fourier transform relate to gradients of functions?

Published on 09 Apr 2026 - 17:37

score 41 · Answer 10 · 2026-04-15 06:13:41

41

Views

$f(x)=\frac{e^{ix^3}}{1+x^2}.$ Is the distribution $(1-\Delta)\hat{f}$ a bounded function?

Published on 15 Apr 2026 - 6:13

score 29 · Answer 11 · 2026-03-25 23:43:59

29

Views

Reversal of Variable Transformation in the Solution of Inhomogeneous Dirichlet PDE

Published on 25 Mar 2026 - 23:43

score 18 · Answer 12 · 2026-04-27 12:05:25

18

Views

Determining whether there is a missing $i$ in Zworski's example of a pseudodifferential operator corresponding to a given symbol

Published on 27 Apr 2026 - 12:05

score 56 · Answer 13 · 2026-04-15 13:01:45

56

Views

When proving that a sequence of functions converges uniformly on compact sets in $\mathbb{R}$, it is sufficient to show uniform convergence on $[a,b]$

Published on 15 Apr 2026 - 13:01

score 65 · Answer 14 · 2026-04-10 12:41:34

65

Views

Fourier transform of Gaussian multiplied with complex Gaussian

Published on 10 Apr 2026 - 12:41

score 180 · Answer 15 · 2026-04-12 16:40:06

180

Views

Plancherel theorem for multi-dimensional discrete Fourier transform

Published on 12 Apr 2026 - 16:40

List Question

Prove the independence of "a" of a Fourier coefficient of a Fourier series calculated over the interval $[-a,a]$

computing $L^p-$norm of nice function.

Positivity of the Fourier transform: prove or disprove that $\operatorname{Re}(\overline{\widehat{u}}(\xi) \widehat{F\circ u}(\xi))\geq0$

Inequality regarding a function and its Fourier transform

If $1/m$ is a Fourier multiplier in $L^p,$ then is $1/(1+m)$ also a Fourier multiplier?

Any constant function is a Fourier Multiplier in $L^p(\mathbb{R}^n)$?

Relation between FT of function and FT of modulus squared function

When is a solution $P(f'(x)) = Q(f(x))$ periodic or double periodic?

How does the multidimensional Fourier transform relate to gradients of functions?

$f(x)=\frac{e^{ix^3}}{1+x^2}.$ Is the distribution $(1-\Delta)\hat{f}$ a bounded function?

Reversal of Variable Transformation in the Solution of Inhomogeneous Dirichlet PDE

Determining whether there is a missing $i$ in Zworski's example of a pseudodifferential operator corresponding to a given symbol

When proving that a sequence of functions converges uniformly on compact sets in $\mathbb{R}$, it is sufficient to show uniform convergence on $[a,b]$

Fourier transform of Gaussian multiplied with complex Gaussian

Plancherel theorem for multi-dimensional discrete Fourier transform

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