Closed curve for an analityc function
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If I have an analityc function $f(z)$ on a domain $B subset mathbb{C}$ and a simple and closed curve $C$ that encloses $B$, and if $|f|$ is constant over C, the $f$ is constant on $B$?
I haven’t found a counterexample but i dont know how to apply the maximum principle or apply some analityc continuation. Please some help with this.
complex-analysis analytic-functions maximum-principle analytic-continuation
asked Nov 18 at 4:17
J.Rodriguez
15310
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up vote
0
down vote
favorite
If I have an analityc function $f(z)$ on a domain $B subset mathbb{C}$ and a simple and closed curve $C$ that encloses $B$, and if $|f|$ is constant over C, the $f$ is constant on $B$?
I haven’t found a counterexample but i dont know how to apply the maximum principle or apply some analityc continuation. Please some help with this.
complex-analysis analytic-functions maximum-principle analytic-continuation
asked Nov 18 at 4:17
J.Rodriguez
15310
2
$f(z) = z$ on $|z| = 1$ ? Otherwise $f(z) =c frac{z+b}{overline{b}z+1}$ with $|b| < 1$ on $|z|=1$
– reuns
Nov 18 at 4:24
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If I have an analityc function $f(z)$ on a domain $B subset mathbb{C}$ and a simple and closed curve $C$ that encloses $B$, and if $|f|$ is constant over C, the $f$ is constant on $B$?
I haven’t found a counterexample but i dont know how to apply the maximum principle or apply some analityc continuation. Please some help with this.
complex-analysis analytic-functions maximum-principle analytic-continuation
asked Nov 18 at 4:17
J.Rodriguez
15310
If I have an analityc function $f(z)$ on a domain $B subset mathbb{C}$ and a simple and closed curve $C$ that encloses $B$, and if $|f|$ is constant over C, the $f$ is constant on $B$?
I haven’t found a counterexample but i dont know how to apply the maximum principle or apply some analityc continuation. Please some help with this.
complex-analysis analytic-functions maximum-principle analytic-continuation
complex-analysis analytic-functions maximum-principle analytic-continuation
asked Nov 18 at 4:17
J.Rodriguez
15310
asked Nov 18 at 4:17
J.Rodriguez
15310
asked Nov 18 at 4:17
J.Rodriguez
15310
asked Nov 18 at 4:17
J.Rodriguez
15310
asked Nov 18 at 4:17
J.Rodriguez
15310
15310
2
$f(z) = z$ on $|z| = 1$ ? Otherwise $f(z) =c frac{z+b}{overline{b}z+1}$ with $|b| < 1$ on $|z|=1$
– reuns
Nov 18 at 4:24
add a comment |
2
$f(z) = z$ on $|z| = 1$ ? Otherwise $f(z) =c frac{z+b}{overline{b}z+1}$ with $|b| < 1$ on $|z|=1$
– reuns
Nov 18 at 4:24
2
2
$f(z) = z$ on $|z| = 1$ ? Otherwise $f(z) =c frac{z+b}{overline{b}z+1}$ with $|b| < 1$ on $|z|=1$
– reuns
Nov 18 at 4:24
$f(z) = z$ on $|z| = 1$ ? Otherwise $f(z) =c frac{z+b}{overline{b}z+1}$ with $|b| < 1$ on $|z|=1$
– reuns
Nov 18 at 4:24
add a comment |
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2
$f(z) = z$ on $|z| = 1$ ? Otherwise $f(z) =c frac{z+b}{overline{b}z+1}$ with $|b| < 1$ on $|z|=1$
– reuns
Nov 18 at 4:24