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Exercise:
Does there exist a non-constant holomorphic map between the given subsets of mathbbC? If yes give a concrete function or give a reason if not. abcliste abc f:mathbbCrightarrow mathbbD abc f:mathbbHrightarrow mathbbD abc f:mathbbCrightarrow mathbbCbackslash i abc f:mathbbDrightarrow mathbbD with the extra condition that f'+i. abcliste

Solution:
abcliste abc No there does not exist such a map since it is always entire and bounded Casaroti-Weierstrass + Liouville abc Yes i.e. fzfracz-iz+i. abc Yes i.e. fze^z+i. abc No. From Cauchy's formula f^nz fracn!pi i_Cfracfxixi-z^n+ddxi we get that |f^| left|frac!pi i_Cfracfxixi^ddxiright| left|fracpi i_Cfracfxixi^ddxiright| &leq fracpi pi r & for gammatre^itheta leq thetaleq pi and r . abcliste
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Exercise:
Does there exist a non-constant holomorphic map between the given subsets of mathbbC? If yes give a concrete function or give a reason if not. abcliste abc f:mathbbCrightarrow mathbbD abc f:mathbbHrightarrow mathbbD abc f:mathbbCrightarrow mathbbCbackslash i abc f:mathbbDrightarrow mathbbD with the extra condition that f'+i. abcliste

Solution:
abcliste abc No there does not exist such a map since it is always entire and bounded Casaroti-Weierstrass + Liouville abc Yes i.e. fzfracz-iz+i. abc Yes i.e. fze^z+i. abc No. From Cauchy's formula f^nz fracn!pi i_Cfracfxixi-z^n+ddxi we get that |f^| left|frac!pi i_Cfracfxixi^ddxiright| left|fracpi i_Cfracfxixi^ddxiright| &leq fracpi pi r & for gammatre^itheta leq thetaleq pi and r . abcliste
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ca, conformal, holomorphic, maps
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(2, default)
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Language
ENG (English)
Type
Calculative / Quantity
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