Question

Putting Analytic function interms of z from x,y

score 142 · Answer 1 · 2017-07-23 18:27:02

142

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Putting Analytic function interms of z from x,y

Published on 23 Jul 2017 - 18:27

score 36 · Answer 2 · 2017-07-25 21:49:01

36

Views

Show $\left| \frac{d^m}{dx^m} e^{-|x|^k} \right| \le C^{m+1} |x|^{2(k-1)}e^{-|x|^k}, \forall |x|>a$

Published on 25 Jul 2017 - 21:49

score 137 · Answer 3 · 2017-07-26 16:39:53

137

Views

Let $g(x)$ be analytic on every interval that does not contain $0$ is $f(t)= E[g(X-t)]$ analytic

Published on 26 Jul 2017 - 16:39

score 541 · Answer 4 · 2017-07-28 14:19:47

541

Views

Other any other versions of identity theorem.

Published on 28 Jul 2017 - 14:19

score 220 · Answer 5 · 2026-03-26 17:14:25

220

Views

Smoothness of $\frac12[W_0(x)+W_{-1}(x)]$ for real $x<0$

Published on 26 Mar 2026 - 17:14

score 1.1k · Answer 6 · 2017-08-03 13:29:07

1.1k

Views

prove that limit function is analytic for sequence of analytic function on compacts subsets of $\Omega$

Published on 03 Aug 2017 - 13:29

score 191 · Answer 7 · 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 128 · Answer 8 · 2017-08-20 10:39:25

let $f:\mathbb {H}\to\mathbb {H}$ holomorphic, show $\Bigg|\frac{f(w)-f(z)}{f(w)-\overline{f(z)}}\Bigg|\leq\bigg|\frac{w-z}{w-\overline{z}}\bigg|$?

score 213 · Answer 9 · 2017-08-25 17:07:46

213

Views

When does a power series decay at infinity?

Published on 25 Aug 2017 - 17:07

score 1.8k · Answer 10 · 2017-08-25 19:36:29

1.8k

Views

For every analytic function $f$ on $G$ (simply connected,open) s.t $f(z) \neq 0, \forall z \in G$, then $\exists$ g analytic in $G$ s.t $g^2 = f$

Published on 25 Aug 2017 - 19:36

score 381 · Answer 11 · 2017-08-26 01:36:07

381

Views

If $f$ analytic in $G$ and $\exists \lambda >0$, $|f(z)| = \lambda, \forall z \in \partial G \Rightarrow \exists z, f(z) = 0$

Published on 26 Aug 2017 - 1:36

score 1.4k · Answer 12 · 2026-03-28 18:16:07

1.4k

Views

Is $z^3 cot(z)$ analytic inside the unit circle ($z \in C$)?

Published on 28 Mar 2026 - 18:16

score 744 · Answer 13 · 2026-03-28 16:04:09

744

Views

Why do you require connection in the open mapping theorem and maximum modulus principle?

Published on 28 Mar 2026 - 16:04

score 901 · Answer 14 · 2017-09-02 19:10:26

901

Views

Prove that the map $z \mapsto \phi (z,w)$ is analytic for each fixed $w$ in a region $G$.

Published on 02 Sep 2017 - 19:10

score 245 · Answer 15 · 2017-09-04 06:48:33

245

Views

Is every locally bounded function asymptotically dominated by a real-analytic function?

Published on 04 Sep 2017 - 6:48

List Question

Putting Analytic function interms of z from x,y

Show $\left| \frac{d^m}{dx^m} e^{-|x|^k} \right| \le C^{m+1} |x|^{2(k-1)}e^{-|x|^k}, \forall |x|>a$

Let $g(x)$ be analytic on every interval that does not contain $0$ is $f(t)= E[g(X-t)]$ analytic

Other any other versions of identity theorem.

Smoothness of $\frac12[W_0(x)+W_{-1}(x)]$ for real $x<0$

prove that limit function is analytic for sequence of analytic function on compacts subsets of $\Omega$

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

let $f:\mathbb {H}\to\mathbb {H}$ holomorphic, show $\Bigg|\frac{f(w)-f(z)}{f(w)-\overline{f(z)}}\Bigg|\leq\bigg|\frac{w-z}{w-\overline{z}}\bigg|$?

When does a power series decay at infinity?

For every analytic function $f$ on $G$ (simply connected,open) s.t $f(z) \neq 0, \forall z \in G$, then $\exists$ g analytic in $G$ s.t $g^2 = f$

If $f$ analytic in $G$ and $\exists \lambda >0$, $|f(z)| = \lambda, \forall z \in \partial G \Rightarrow \exists z, f(z) = 0$

Is $z^3 cot(z)$ analytic inside the unit circle ($z \in C$)?

Why do you require connection in the open mapping theorem and maximum modulus principle?

Prove that the map $z \mapsto \phi (z,w)$ is analytic for each fixed $w$ in a region $G$.

Is every locally bounded function asymptotically dominated by a real-analytic function?

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