Question

Trying to compute limit of singular integrals : $L= \lim_{s\to 1}(1-s)\int_{\Omega}\frac{(u(x)-u(y))}{|x-y|^{d+2s}} d y.$

score 540 · Answer 1 · 2026-03-25 00:04:25

540

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Trying to compute limit of singular integrals : $L= \lim_{s\to 1}(1-s)\int_{\Omega}\frac{(u(x)-u(y))}{|x-y|^{d+2s}} d y.$

Published on 25 Mar 2026 - 0:04

score 290 · Answer 2 · 2026-03-25 00:07:51

290

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What is this singular distribution $T(\phi)(x) = \int_{\mathbb{R}^n} \frac{\phi(y)}{|x-y|^n} \mathrm{d}y$?

Published on 25 Mar 2026 - 0:07

score 52 · Answer 3 · 2026-04-10 23:29:05

52

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Reference request Singular Integrals

Published on 10 Apr 2026 - 23:29

score 730 · Answer 4 · 2026-03-24 23:58:57

730

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Integral involving convolution with Poisson kernel.

Published on 24 Mar 2026 - 23:58

score 107 · Answer 5 · 2026-03-25 00:07:56

107

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Is the function $\frac{1}{\sqrt{|x_1|}}$integrable on the unit sphere $S^{n-1}\subset\mathbb{R}^n$?

Published on 25 Mar 2026 - 0:07

score 81 · Answer 6 · 2026-03-25 00:07:39

81

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How to make sense of the Fourier transform of this distribution

Published on 25 Mar 2026 - 0:07

score 74 · Answer 7 · 2026-03-25 00:01:34

74

Views

Question about the principal value of some integral

Published on 25 Mar 2026 - 0:01

score 112 · Answer 8 · 2026-03-25 00:02:19

112

Views

exact or numerical value of an improper integral

Published on 25 Mar 2026 - 0:02

score 70 · Answer 9 · 2026-03-24 23:59:34

70

Views

Is this function square-integrable? Able to be Fourier expanded?

Published on 24 Mar 2026 - 23:59

score 235 · Answer 10 · 2026-04-11 00:50:56

235

Views

Cauchy singular integral operator

Published on 11 Apr 2026 - 0:50

score 215 · Answer 11 · 2026-04-12 00:23:00

215

Views

Numerically integrate an improper integral involving product of two bessel functions and a singularity

Published on 12 Apr 2026 - 0:23

score 80 · Answer 12 · 2026-03-25 00:06:33

80

Views

Asymptotic behavior of oscillatory Hilbert transform

Published on 25 Mar 2026 - 0:06

score 739 · Answer 13 · 2026-03-27 06:58:55

739

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norm of a singular integral operator

Published on 27 Mar 2026 - 6:58

score 422 · Answer 14 · 2026-03-25 00:07:48

422

Views

integration concerning Fourier transform of homogeneous kernel(of degree 0)

Published on 25 Mar 2026 - 0:07

score 72 · Answer 15 · 2026-03-25 00:04:25

72

Views

Expression for integral of $\omega * \hat f (\omega)$, where $\hat f$ is the (one-sided) cosine transform of f

Published on 25 Mar 2026 - 0:04

List Question

Trying to compute limit of singular integrals : $L= \lim_{s\to 1}(1-s)\int_{\Omega}\frac{(u(x)-u(y))}{|x-y|^{d+2s}} d y.$

What is this singular distribution $T(\phi)(x) = \int_{\mathbb{R}^n} \frac{\phi(y)}{|x-y|^n} \mathrm{d}y$?

Reference request Singular Integrals

Integral involving convolution with Poisson kernel.

Is the function $\frac{1}{\sqrt{|x_1|}}$integrable on the unit sphere $S^{n-1}\subset\mathbb{R}^n$?

How to make sense of the Fourier transform of this distribution

Question about the principal value of some integral

exact or numerical value of an improper integral

Is this function square-integrable? Able to be Fourier expanded?

Cauchy singular integral operator

Numerically integrate an improper integral involving product of two bessel functions and a singularity

Asymptotic behavior of oscillatory Hilbert transform

norm of a singular integral operator

integration concerning Fourier transform of homogeneous kernel(of degree 0)

Expression for integral of $\omega * \hat f (\omega)$, where $\hat f$ is the (one-sided) cosine transform of f

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