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An example of holomorph functions
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Make an examples $f:Bbb{C}toBbb{C}$ holomorph (If it exists) with the properties:(Justify your answer)
$f(x)=x^2$ for all $xinBbb{R}$ and $f(iy)=y^4$ for all $yinBbb{R}$.
My attemp for (1) was $f(z)=(dfrac{z+bar{z}}{2})^2+(dfrac{z-bar{z}}{2i})^4$
but I do not know how I can prove or disprove it.
complex-analysis
asked Jan 9 at 15:50
seyedseyed
566
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add a comment |
$begingroup$
Make an examples $f:Bbb{C}toBbb{C}$ holomorph (If it exists) with the properties:(Justify your answer)
$f(x)=x^2$ for all $xinBbb{R}$ and $f(iy)=y^4$ for all $yinBbb{R}$.
My attemp for (1) was $f(z)=(dfrac{z+bar{z}}{2})^2+(dfrac{z-bar{z}}{2i})^4$
but I do not know how I can prove or disprove it.
complex-analysis
asked Jan 9 at 15:50
seyedseyed
566
$endgroup$
add a comment |
$begingroup$
Make an examples $f:Bbb{C}toBbb{C}$ holomorph (If it exists) with the properties:(Justify your answer)
$f(x)=x^2$ for all $xinBbb{R}$ and $f(iy)=y^4$ for all $yinBbb{R}$.
My attemp for (1) was $f(z)=(dfrac{z+bar{z}}{2})^2+(dfrac{z-bar{z}}{2i})^4$
but I do not know how I can prove or disprove it.
complex-analysis
asked Jan 9 at 15:50
seyedseyed
566
$endgroup$
Make an examples $f:Bbb{C}toBbb{C}$ holomorph (If it exists) with the properties:(Justify your answer)
$f(x)=x^2$ for all $xinBbb{R}$ and $f(iy)=y^4$ for all $yinBbb{R}$.
My attemp for (1) was $f(z)=(dfrac{z+bar{z}}{2})^2+(dfrac{z-bar{z}}{2i})^4$
but I do not know how I can prove or disprove it.
complex-analysis
complex-analysis
asked Jan 9 at 15:50
seyedseyed
566
asked Jan 9 at 15:50
seyedseyed
566
edited Jan 9 at 16:08
seyed
asked Jan 9 at 15:50
seyedseyed
566
asked Jan 9 at 15:50
seyedseyed
566
asked Jan 9 at 15:50
seyedseyed
566
566
add a comment |
add a comment |
1 Answer
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Your example doesn't work, since your functions is not holomorphic. By the identity theorem, if $(forall zinmathbb{R}):f(x)=x^2$, then $(forall zinmathbb{C}):f(x)=x^2$. So, there is no such function.
You should delete your two other questions and ask them as two individual questions, showing your effort. Otherwise, this question will likely be closed as “too broad”.
answered Jan 9 at 16:05
José Carlos SantosJosé Carlos Santos
158k22126228
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1 Answer
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1 Answer
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active
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$begingroup$
Your example doesn't work, since your functions is not holomorphic. By the identity theorem, if $(forall zinmathbb{R}):f(x)=x^2$, then $(forall zinmathbb{C}):f(x)=x^2$. So, there is no such function.
You should delete your two other questions and ask them as two individual questions, showing your effort. Otherwise, this question will likely be closed as “too broad”.
answered Jan 9 at 16:05
José Carlos SantosJosé Carlos Santos
158k22126228
$endgroup$
add a comment |
$begingroup$
Your example doesn't work, since your functions is not holomorphic. By the identity theorem, if $(forall zinmathbb{R}):f(x)=x^2$, then $(forall zinmathbb{C}):f(x)=x^2$. So, there is no such function.
You should delete your two other questions and ask them as two individual questions, showing your effort. Otherwise, this question will likely be closed as “too broad”.
answered Jan 9 at 16:05
José Carlos SantosJosé Carlos Santos
158k22126228
$endgroup$
add a comment |
$begingroup$
Your example doesn't work, since your functions is not holomorphic. By the identity theorem, if $(forall zinmathbb{R}):f(x)=x^2$, then $(forall zinmathbb{C}):f(x)=x^2$. So, there is no such function.
You should delete your two other questions and ask them as two individual questions, showing your effort. Otherwise, this question will likely be closed as “too broad”.
answered Jan 9 at 16:05
José Carlos SantosJosé Carlos Santos
158k22126228
$endgroup$
Your example doesn't work, since your functions is not holomorphic. By the identity theorem, if $(forall zinmathbb{R}):f(x)=x^2$, then $(forall zinmathbb{C}):f(x)=x^2$. So, there is no such function.
You should delete your two other questions and ask them as two individual questions, showing your effort. Otherwise, this question will likely be closed as “too broad”.
answered Jan 9 at 16:05
José Carlos SantosJosé Carlos Santos
158k22126228
answered Jan 9 at 16:05
José Carlos SantosJosé Carlos Santos
158k22126228
answered Jan 9 at 16:05
José Carlos SantosJosé Carlos Santos
158k22126228
answered Jan 9 at 16:05
José Carlos SantosJosé Carlos Santos
158k22126228
158k22126228
add a comment |
add a comment |
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