Question

$f$ is non-vanishing holomorphic function on open unit disc such that $|f(z)|\to1$ as $|z|\to1$. Is $f$ constant?

score 1.3k · Answer 1 · 2019-04-26 15:57:23

1.3k

Views

$f$ is non-vanishing holomorphic function on open unit disc such that $|f(z)|\to1$ as $|z|\to1$. Is $f$ constant?

Published on 26 Apr 2019 - 15:57

score 247 · Answer 2 · 2019-05-03 12:16:20

247

Views

$f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$ if $\lim_{z\to\infty}f(z)=0$ and $f$ is analytic in $|z|\ge1$

Published on 03 May 2019 - 12:16

score 312 · Answer 3 · 2026-03-17 23:29:13

312

Views

Winding numbers in complex analysis and Cauchy-Goursat theorem

Published on 17 Mar 2026 - 23:29

score 114 · Answer 4 · 2026-03-25 04:59:47

114

Views

Why does $\int_{C_2-C_1} {f(w)-f(z)\over w-z}dw =0$ where $f$ is analytic in an annulus?

Published on 25 Mar 2026 - 4:59

score 68 · Answer 5 · 2019-05-19 17:01:36

68

Views

Flaws with Cauchy's Integral Formula proof

Published on 19 May 2019 - 17:01

score 147 · Answer 6 · 2026-03-25 18:53:51

147

Views

Using Cauchy's Estimate for Lower Bound of Entire Function

Published on 25 Mar 2026 - 18:53

score 71 · Answer 7 · 2026-03-25 07:44:40

71

Views

Explanation of coefficient when evaluating contour around a branch for fractional version of Cauchy's Integral Formula

Published on 25 Mar 2026 - 7:44

score 65 · Answer 8 · 2019-05-25 18:44:20

65

Views

Cauchy's integral Theorem proof clarify

Published on 25 May 2019 - 18:44

score 439 · Answer 9 · 2019-05-25 21:40:15

439

Views

Cauchy integral of $\frac{1}{z}$ over closed curve

Published on 25 May 2019 - 21:40

score 105 · Answer 10 · 2019-05-26 06:31:32

105

Views

Let $γ$ be sum of two line segments connecting $-2$ with $iy$ and $iy$ with $2$, where $y$ is fixed parameter. Write explicit parametrization for $γ$.

Published on 26 May 2019 - 6:31

score 141 · Answer 11 · 2019-05-28 20:30:53

141

Views

Prove that a function which is analytic in unit circle and satisfies $f(0)=1$ and $f(z) \ge 1 + |z|^ 2$ doesn't exist

Published on 28 May 2019 - 20:30

score 215 · Answer 12 · 2019-05-29 12:19:11

215

Views

Cauchy's Integral Formula and number of zeros

Published on 29 May 2019 - 12:19

score 59 · Answer 13 · 2019-05-30 09:22:54

59

Views

Standard inequality and Cauchy integral formula

Published on 30 May 2019 - 9:22

score 58 · Answer 14 · 2019-05-30 21:51:52

58

Views

Compute $\oint_{\partial D_3(0)}\frac{\cos(z+4)}{z^2+1}dz$

Published on 30 May 2019 - 21:51

score 83 · Answer 15 · 2019-06-04 22:34:21

83

Views

if $\sup_{0<r<1} \int_0^{2\pi} |f(re^{i t})|^2 dt < \infty$ then $\sum{|a_n|^2} <\infty$

Published on 04 Jun 2019 - 22:34

List Question

$f$ is non-vanishing holomorphic function on open unit disc such that $|f(z)|\to1$ as $|z|\to1$. Is $f$ constant?

$f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$ if $\lim_{z\to\infty}f(z)=0$ and $f$ is analytic in $|z|\ge1$

Winding numbers in complex analysis and Cauchy-Goursat theorem

Why does $\int_{C_2-C_1} {f(w)-f(z)\over w-z}dw =0$ where $f$ is analytic in an annulus?

Flaws with Cauchy's Integral Formula proof

Using Cauchy's Estimate for Lower Bound of Entire Function

Explanation of coefficient when evaluating contour around a branch for fractional version of Cauchy's Integral Formula

Cauchy's integral Theorem proof clarify

Cauchy integral of $\frac{1}{z}$ over closed curve

Let $γ$ be sum of two line segments connecting $-2$ with $iy$ and $iy$ with $2$, where $y$ is fixed parameter. Write explicit parametrization for $γ$.

Prove that a function which is analytic in unit circle and satisfies $f(0)=1$ and $f(z) \ge 1 + |z|^ 2$ doesn't exist

Cauchy's Integral Formula and number of zeros

Standard inequality and Cauchy integral formula

Compute $\oint_{\partial D_3(0)}\frac{\cos(z+4)}{z^2+1}dz$

if $\sup_{0<r<1} \int_0^{2\pi} |f(re^{i t})|^2 dt < \infty$ then $\sum{|a_n|^2} <\infty$

Trending Questions

Popular # Hahtags

Popular Questions