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Can an holomorphic function have a convergent sequence of points in its domain with only real values?
An equation with Gamma Euler function in critical stripsurjective holomorphic function in a special domainSpecifying a holomorphic function by a sequence of valuesComposition of a holomorphic function with a normal family of holomorphic functions.On every simply connected domain, there exists a holomorphic function with no analytic continuation.Can a complex function be holomorphic only on a proper closed subset of $mathbbC$?Sequence of holomorphic function and its derivativeProof the continuity of a function.A sequence of holomorphic functions $f_n$ uniformly convergent on boundary of open set.Holomorphic function in a region symmetric about origin which takes real values on some non-empty interval intersection with the regionSquare Root of a Holomorphic Function
$begingroup$
Let $D subset mathbbC$ be a open subset of the complex plane
Let $f: D to mathbbC$ be a holomorphic function
Let $z_n_n in mathbbN subset D$ be a sequence in $D$ such that $z_n to s in D$ and we have $f(z_n) to f(s)=0$
My question is:
Is there a subsequence $z_n_k_k in mathbbN$ such that $forall k in mathbbN: Im(f(z_n_k)) neq 0$
Thanks.
complex-analysis holomorphic-functions
asked Mar 12 at 10:55
Matey MathMatey Math
852514
$endgroup$
add a comment |
$begingroup$
Let $D subset mathbbC$ be a open subset of the complex plane
Let $f: D to mathbbC$ be a holomorphic function
Let $z_n_n in mathbbN subset D$ be a sequence in $D$ such that $z_n to s in D$ and we have $f(z_n) to f(s)=0$
My question is:
Is there a subsequence $z_n_k_k in mathbbN$ such that $forall k in mathbbN: Im(f(z_n_k)) neq 0$
Thanks.
complex-analysis holomorphic-functions
asked Mar 12 at 10:55
Matey MathMatey Math
852514
$endgroup$
add a comment |
$begingroup$
Let $D subset mathbbC$ be a open subset of the complex plane
Let $f: D to mathbbC$ be a holomorphic function
Let $z_n_n in mathbbN subset D$ be a sequence in $D$ such that $z_n to s in D$ and we have $f(z_n) to f(s)=0$
My question is:
Is there a subsequence $z_n_k_k in mathbbN$ such that $forall k in mathbbN: Im(f(z_n_k)) neq 0$
Thanks.
complex-analysis holomorphic-functions
asked Mar 12 at 10:55
Matey MathMatey Math
852514
$endgroup$
Let $D subset mathbbC$ be a open subset of the complex plane
Let $f: D to mathbbC$ be a holomorphic function
Let $z_n_n in mathbbN subset D$ be a sequence in $D$ such that $z_n to s in D$ and we have $f(z_n) to f(s)=0$
My question is:
Is there a subsequence $z_n_k_k in mathbbN$ such that $forall k in mathbbN: Im(f(z_n_k)) neq 0$
Thanks.
complex-analysis holomorphic-functions
complex-analysis holomorphic-functions
asked Mar 12 at 10:55
Matey MathMatey Math
852514
asked Mar 12 at 10:55
Matey MathMatey Math
852514
asked Mar 12 at 10:55
Matey MathMatey Math
852514
asked Mar 12 at 10:55
Matey MathMatey Math
852514
asked Mar 12 at 10:55
Matey MathMatey Math
852514
852514
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Well... Not necessarily. Let $f(z)=z$ and $z_n=1/n$ for example.
answered Mar 12 at 11:03
Giuseppe NegroGiuseppe Negro
17.5k332126
$endgroup$
$begingroup$
Thanks for your answer @GiuseppeNegro
$endgroup$
– Matey Math
Mar 12 at 11:07
$begingroup$
@MateyMath: you are welcome but it is really trivial. Probably you are not asking the right question.
$endgroup$
– Giuseppe Negro
Mar 12 at 11:20
$begingroup$
you are right it was a trivial attempt to solve this math.stackexchange.com/questions/3142477/…
$endgroup$
– Matey Math
Mar 12 at 11:42
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Well... Not necessarily. Let $f(z)=z$ and $z_n=1/n$ for example.
answered Mar 12 at 11:03
Giuseppe NegroGiuseppe Negro
17.5k332126
$endgroup$
$begingroup$
Thanks for your answer @GiuseppeNegro
$endgroup$
– Matey Math
Mar 12 at 11:07
$begingroup$
@MateyMath: you are welcome but it is really trivial. Probably you are not asking the right question.
$endgroup$
– Giuseppe Negro
Mar 12 at 11:20
$begingroup$
you are right it was a trivial attempt to solve this math.stackexchange.com/questions/3142477/…
$endgroup$
– Matey Math
Mar 12 at 11:42
add a comment |
$begingroup$
Well... Not necessarily. Let $f(z)=z$ and $z_n=1/n$ for example.
answered Mar 12 at 11:03
Giuseppe NegroGiuseppe Negro
17.5k332126
$endgroup$
$begingroup$
Thanks for your answer @GiuseppeNegro
$endgroup$
– Matey Math
Mar 12 at 11:07
$begingroup$
@MateyMath: you are welcome but it is really trivial. Probably you are not asking the right question.
$endgroup$
– Giuseppe Negro
Mar 12 at 11:20
$begingroup$
you are right it was a trivial attempt to solve this math.stackexchange.com/questions/3142477/…
$endgroup$
– Matey Math
Mar 12 at 11:42
add a comment |
$begingroup$
Well... Not necessarily. Let $f(z)=z$ and $z_n=1/n$ for example.
answered Mar 12 at 11:03
Giuseppe NegroGiuseppe Negro
17.5k332126
$endgroup$
Well... Not necessarily. Let $f(z)=z$ and $z_n=1/n$ for example.
answered Mar 12 at 11:03
Giuseppe NegroGiuseppe Negro
17.5k332126
answered Mar 12 at 11:03
Giuseppe NegroGiuseppe Negro
17.5k332126
answered Mar 12 at 11:03
Giuseppe NegroGiuseppe Negro
17.5k332126
answered Mar 12 at 11:03
Giuseppe NegroGiuseppe Negro
17.5k332126
17.5k332126
$begingroup$
Thanks for your answer @GiuseppeNegro
$endgroup$
– Matey Math
Mar 12 at 11:07
$begingroup$
@MateyMath: you are welcome but it is really trivial. Probably you are not asking the right question.
$endgroup$
– Giuseppe Negro
Mar 12 at 11:20
$begingroup$
you are right it was a trivial attempt to solve this math.stackexchange.com/questions/3142477/…
$endgroup$
– Matey Math
Mar 12 at 11:42
add a comment |
$begingroup$
Thanks for your answer @GiuseppeNegro
$endgroup$
– Matey Math
Mar 12 at 11:07
$begingroup$
@MateyMath: you are welcome but it is really trivial. Probably you are not asking the right question.
$endgroup$
– Giuseppe Negro
Mar 12 at 11:20
$begingroup$
you are right it was a trivial attempt to solve this math.stackexchange.com/questions/3142477/…
$endgroup$
– Matey Math
Mar 12 at 11:42
$begingroup$
Thanks for your answer @GiuseppeNegro
$endgroup$
– Matey Math
Mar 12 at 11:07
$begingroup$
Thanks for your answer @GiuseppeNegro
$endgroup$
– Matey Math
Mar 12 at 11:07
$begingroup$
@MateyMath: you are welcome but it is really trivial. Probably you are not asking the right question.
$endgroup$
– Giuseppe Negro
Mar 12 at 11:20
$begingroup$
@MateyMath: you are welcome but it is really trivial. Probably you are not asking the right question.
$endgroup$
– Giuseppe Negro
Mar 12 at 11:20
$begingroup$
you are right it was a trivial attempt to solve this math.stackexchange.com/questions/3142477/…
$endgroup$
– Matey Math
Mar 12 at 11:42
$begingroup$
you are right it was a trivial attempt to solve this math.stackexchange.com/questions/3142477/…
$endgroup$
– Matey Math
Mar 12 at 11:42
add a comment |
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