Question

How to show $\|e^{ikx}-e^{ix}\|_{L^{1}}$ does not converge to $0$ when $k\rightarrow\infty$?

score 70 · Answer 1 · 2020-03-06 06:58:58

70

Views

How to show $\|e^{ikx}-e^{ix}\|_{L^{1}}$ does not converge to $0$ when $k\rightarrow\infty$?

Published on 06 Mar 2020 - 6:58

score 74 · Answer 2 · 2020-03-06 11:23:45

74

Views

Show that for holomorphic $f$ on an open set $U \subseteq \mathbb{C}$ $\int_{\gamma}\frac{f'(z)}{f(z)}dz = 0$

Published on 06 Mar 2020 - 11:23

score 64 · Answer 3 · 2020-03-09 10:42:52

64

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Do line integrals in a convex domain vanish for a function that is only continuous?

Published on 09 Mar 2020 - 10:42

score 83 · Answer 4 · 2020-03-09 21:25:18

83

Views

How to evaluate $\int_0^{2\pi} e^{e^{i\theta}}{d\theta}$?

Published on 09 Mar 2020 - 21:25

score 582 · Answer 5 · 2026-03-26 09:44:52

582

Views

Gaussian integral with complex argument

Published on 26 Mar 2026 - 9:44

score 162 · Answer 6 · 2020-03-10 13:58:07

162

Views

Complex integration of real poles of multiplicity 2

Published on 10 Mar 2020 - 13:58

score 162 · Answer 7 · 2020-03-11 14:53:34

162

Views

How to compute $\int_0^\infty \frac{\log(2+x^2)}{4+x^2}\,\mathrm dx$

Published on 11 Mar 2020 - 14:53

score 51 · Answer 8 · 2026-03-26 10:56:31

51

Views

How to solve this integral (complex variables - green's function)

Published on 26 Mar 2026 - 10:56

score 197 · Answer 9 · 2020-03-13 08:47:37

197

Views

If $\frac{\partial u}{\partial \overline{z}}=f$ and $|u(z)|$ goes to $0$ as $z\to \infty$, then $u$ is of this form.

Published on 13 Mar 2020 - 8:47

score 232 · Answer 10 · 2020-03-13 09:06:53

If $u\in C_{0}^{\infty}(\mathbb{C})$ and $\frac{\partial u}{\partial\overline{z}}$ is a real valued nonnegative function, then $u\equiv 0$.

score 437 · Answer 11 · 2020-03-14 20:32:04

437

Views

Prove that this complex integral converges

Published on 14 Mar 2020 - 20:32

score 301 · Answer 12 · 2026-03-25 06:25:01

301

Views

$L^{p}$ spaces for complex measures

Published on 25 Mar 2026 - 6:25

score 117 · Answer 13 · 2020-03-19 07:22:18

117

Views

How to show that z/(z^2+1) is less than or equal to 1/2 when dom(z) is the line segment from 2 to 2+i? (ML formula for integration)

Published on 19 Mar 2020 - 7:22

score 380 · Answer 14 · 2026-03-25 19:00:58

380

Views

Laplace Integral for Legendre Polynomial

Published on 25 Mar 2026 - 19:00

score 84 · Answer 15 · 2020-03-21 11:46:37

84

Views

I want to show that $\frac{i}{2\pi}\int^{2\pi}_0e^{(a+b)\cos\theta}\sin((a-b)\sin\theta-n\theta)d\theta = 0$

Published on 21 Mar 2020 - 11:46

List Question

How to show $\|e^{ikx}-e^{ix}\|_{L^{1}}$ does not converge to $0$ when $k\rightarrow\infty$?

Show that for holomorphic $f$ on an open set $U \subseteq \mathbb{C}$ $\int_{\gamma}\frac{f'(z)}{f(z)}dz = 0$

Do line integrals in a convex domain vanish for a function that is only continuous?

How to evaluate $\int_0^{2\pi} e^{e^{i\theta}}{d\theta}$?

Gaussian integral with complex argument

Complex integration of real poles of multiplicity 2

How to compute $\int_0^\infty \frac{\log(2+x^2)}{4+x^2}\,\mathrm dx$

How to solve this integral (complex variables - green's function)

If $\frac{\partial u}{\partial \overline{z}}=f$ and $|u(z)|$ goes to $0$ as $z\to \infty$, then $u$ is of this form.

If $u\in C_{0}^{\infty}(\mathbb{C})$ and $\frac{\partial u}{\partial\overline{z}}$ is a real valued nonnegative function, then $u\equiv 0$.

Prove that this complex integral converges

$L^{p}$ spaces for complex measures

How to show that z/(z^2+1) is less than or equal to 1/2 when dom(z) is the line segment from 2 to 2+i? (ML formula for integration)

Laplace Integral for Legendre Polynomial

I want to show that $\frac{i}{2\pi}\int^{2\pi}_0e^{(a+b)\cos\theta}\sin((a-b)\sin\theta-n\theta)d\theta = 0$

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