Question

Why $(2\pi x)^\alpha f(x)(2\pi i\xi)^\beta e^{-2i\pi x\cdot \xi}=(\partial _x)^\beta [(2\pi x)^\alpha f(x)]e^{-2i\pi x\cdot \xi}$?

score 53 · Answer 1 · 2016-07-03 17:22:35

53

Views

Why $(2\pi x)^\alpha f(x)(2\pi i\xi)^\beta e^{-2i\pi x\cdot \xi}=(\partial _x)^\beta [(2\pi x)^\alpha f(x)]e^{-2i\pi x\cdot \xi}$?

Published on 03 Jul 2016 - 17:22

score 529 · Answer 2 · 2016-07-04 15:41:01

529

Views

The equivalence of the two definitions of fractional Laplacian

Published on 04 Jul 2016 - 15:41

score 142 · Answer 3 · 2016-07-05 08:26:30

142

Views

Are holder space dense in $L^p$ ? or in Schwarz space?

Published on 05 Jul 2016 - 8:26

score 800 · Answer 4 · 2016-07-05 13:45:29

800

Views

Pointwise convergence of Fourier series in two dimensions

Published on 05 Jul 2016 - 13:45

score 48 · Answer 5 · 2013-04-04 18:12:34

48

Views

Given $\widehat{\varphi} = \chi_{[-1/2,1/2]}$, show the system $\{\varphi(2^v x)\}_{v \in \mathbb{Z}}$ is not orthogonal

Published on 04 Apr 2013 - 18:12

score 264 · Answer 6 · 2013-04-05 08:13:53

264

Views

Identity involving partial sums of Fourier series

Published on 05 Apr 2013 - 8:13

score 255 · Answer 7 · 2013-04-08 05:07:31

255

Views

Lorentz Space property: $\left\| f \right\|_{L^{q,s}} \leq \lim\limits_{n\to\infty} \| f_n \|_{L^{q,s}}$

Published on 08 Apr 2013 - 5:07

score 95 · Answer 8 · 2013-04-10 01:54:00

95

Views

Does $|T(f) - T(g)| \leq |T(f-g)|$ hold for a sublinear operator $T$?

Published on 10 Apr 2013 - 1:54

score 805 · Answer 9 · 2013-04-13 07:10:20

805

Views

Showing a Schwartz Function Bound

Published on 13 Apr 2013 - 7:10

score 154 · Answer 10 · 2013-04-18 19:00:24

154

Views

Why does this inequality for all characteristic functions imply it for simple functions?

Published on 18 Apr 2013 - 19:00

score 110 · Answer 11 · 2026-04-01 20:07:20

110

Views

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Published on 01 Apr 2026 - 20:07

score 25 · Answer 12 · 2013-04-22 17:41:04

25

Views

An approximation of lengths dealing with elements of cubes. Show $|x-y| \approx \ell(Q) + |x - c_Q|$.

Published on 22 Apr 2013 - 17:41

score 602 · Answer 13 · 2013-04-23 07:54:06

602

Views

DFT in complex form and Trigonometric Polynomial Interpolation: why different dimensions of basis vectors set?

Published on 23 Apr 2013 - 7:54

score 1.5k · Answer 14 · 2026-04-01 20:00:36

1.5k

Views

Mean Value Property of Harmonic Function on a Square

Published on 01 Apr 2026 - 20:00

score 436 · Answer 15 · 2013-04-26 01:05:37

436

Views

Measure of the boundary of a union of cubes.

Published on 26 Apr 2013 - 1:05

List Question

Why $(2\pi x)^\alpha f(x)(2\pi i\xi)^\beta e^{-2i\pi x\cdot \xi}=(\partial _x)^\beta [(2\pi x)^\alpha f(x)]e^{-2i\pi x\cdot \xi}$?

The equivalence of the two definitions of fractional Laplacian

Are holder space dense in $L^p$ ? or in Schwarz space?

Pointwise convergence of Fourier series in two dimensions

Given $\widehat{\varphi} = \chi_{[-1/2,1/2]}$, show the system $\{\varphi(2^v x)\}_{v \in \mathbb{Z}}$ is not orthogonal

Identity involving partial sums of Fourier series

Lorentz Space property: $\left\| f \right\|_{L^{q,s}} \leq \lim\limits_{n\to\infty} \| f_n \|_{L^{q,s}}$

Does $|T(f) - T(g)| \leq |T(f-g)|$ hold for a sublinear operator $T$?

Showing a Schwartz Function Bound

Why does this inequality for all characteristic functions imply it for simple functions?

Extracting Harmonic series components

An approximation of lengths dealing with elements of cubes. Show $|x-y| \approx \ell(Q) + |x - c_Q|$.

DFT in complex form and Trigonometric Polynomial Interpolation: why different dimensions of basis vectors set?

Mean Value Property of Harmonic Function on a Square

Measure of the boundary of a union of cubes.

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