Question

Reference for some basic statements on operator-valued analytic functions

score 530 · Answer 1 · 2017-07-26 09:01:40

530

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Reference for some basic statements on operator-valued analytic functions

Published on 26 Jul 2017 - 9:01

score 4.9k · Answer 2 · 2017-07-26 17:36:02

4.9k

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Is a function analytic iff it has antiderivative?

Published on 26 Jul 2017 - 17:36

score 218 · Answer 3 · 2017-07-27 07:13:18

218

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Does there exists non-constant entire function with the following conditions?

Published on 27 Jul 2017 - 7:13

score 2.3k · Answer 4 · 2026-03-27 08:41:57

2.3k

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If $f: \mathbb{C} \to \mathbb{C}$ is continuous and analytic off $[-1,1]$ then is entire.

Published on 27 Mar 2026 - 8:41

score 542 · Answer 5 · 2026-03-29 12:12:02

542

Views

Other any other versions of identity theorem.

Published on 29 Mar 2026 - 12:12

score 142 · Answer 6 · 2017-07-28 23:35:20

142

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Expansion of $x\mapsto\left(\frac \pi 2 + \arcsin x\right)^2$ in powers of $x+1$

Published on 28 Jul 2017 - 23:35

score 54 · Answer 7 · 2017-08-02 11:33:18

54

Views

Modular forms half integral weight: Change of multiplicatorsystem for $f \mapsto f \vert N^{-1}$

Published on 02 Aug 2017 - 11:33

score 180 · Answer 8 · 2026-03-25 10:58:55

180

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Show that $g(w) = \frac{1}{2\pi i}\int_{\gamma}\frac{zf'(z)}{f(z) - w}dz$ is analytic and discuss the properties of $g$.

Published on 25 Mar 2026 - 10:58

score 64 · Answer 9 · 2017-08-04 06:59:58

64

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Given that $z = 0$ and $z = 2$ are simple poles of $f$, and $\int_{|z| = 1} f(z) dz = 1$ and $\int_{|z| = 3} f(z) dz = 0$, find $f$

Published on 04 Aug 2017 - 6:59

score 78 · Answer 10 · 2017-08-08 00:51:19

78

Views

Entire function satisfying a growth estimate is periodic

Published on 08 Aug 2017 - 0:51

score 317 · Answer 11 · 2026-03-29 03:27:37

317

Views

Find the analytic solution to this second order inhomogenous difference equation

Published on 29 Mar 2026 - 3:27

score 1.1k · Answer 12 · 2026-03-28 16:44:17

1.1k

Views

Singularities of $\frac{z^2-\pi^2}{\sin(z)}$ and $\frac{z}{e^z-1}$

Published on 28 Mar 2026 - 16:44

score 191 · Answer 13 · 2026-03-27 07:18:50

191

Views

Is there a generalization of the convergence radius of analytic functions to higher dimension?

Published on 27 Mar 2026 - 7:18

score 1.2k · Answer 14 · 2026-03-27 08:45:56

1.2k

Views

Let $f$ be an entire function, show that the following conditions imply that $f$ is constant.

Published on 27 Mar 2026 - 8:45

score 101 · Answer 15 · 2017-08-20 02:29:48

101

Views

Suppose that $f$ is analytic in $\{z \in \mathbb{C}: 0 < |z| < 1\}$ with essential singularity at $0$.

Published on 20 Aug 2017 - 2:29

List Question

Reference for some basic statements on operator-valued analytic functions

Is a function analytic iff it has antiderivative?

Does there exists non-constant entire function with the following conditions?

If $f: \mathbb{C} \to \mathbb{C}$ is continuous and analytic off $[-1,1]$ then is entire.

Other any other versions of identity theorem.

Expansion of $x\mapsto\left(\frac \pi 2 + \arcsin x\right)^2$ in powers of $x+1$

Modular forms half integral weight: Change of multiplicatorsystem for $f \mapsto f \vert N^{-1}$

Show that $g(w) = \frac{1}{2\pi i}\int_{\gamma}\frac{zf'(z)}{f(z) - w}dz$ is analytic and discuss the properties of $g$.

Given that $z = 0$ and $z = 2$ are simple poles of $f$, and $\int_{|z| = 1} f(z) dz = 1$ and $\int_{|z| = 3} f(z) dz = 0$, find $f$

Entire function satisfying a growth estimate is periodic

Find the analytic solution to this second order inhomogenous difference equation

Singularities of $\frac{z^2-\pi^2}{\sin(z)}$ and $\frac{z}{e^z-1}$

Is there a generalization of the convergence radius of analytic functions to higher dimension?

Let $f$ be an entire function, show that the following conditions imply that $f$ is constant.

Suppose that $f$ is analytic in $\{z \in \mathbb{C}: 0 < |z| < 1\}$ with essential singularity at $0$.

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