Existence of the limit of a bounded analytic function
$begingroup$
Let $X$ be a Banach space and let $Usubsetmathbb{C}
$ be open. If we have an analytic function $f:Usetminus left{ 0right}
rightarrow X$ such that $underset{xin Usetminus left{ 0right} }{sup
}leftVert fleft( xright) rightVert <infty ,$ can we say that the
limit $underset{xrightarrow 0}{lim }fleft( xright) $ exists. Thank you !
complex-analysis functional-analysis limits continuity analytic-functions
asked Jan 13 at 23:00
Djalal OunadjelaDjalal Ounadjela
29818
$endgroup$
add a comment |
$begingroup$
Let $X$ be a Banach space and let $Usubsetmathbb{C}
$ be open. If we have an analytic function $f:Usetminus left{ 0right}
rightarrow X$ such that $underset{xin Usetminus left{ 0right} }{sup
}leftVert fleft( xright) rightVert <infty ,$ can we say that the
limit $underset{xrightarrow 0}{lim }fleft( xright) $ exists. Thank you !
complex-analysis functional-analysis limits continuity analytic-functions
asked Jan 13 at 23:00
Djalal OunadjelaDjalal Ounadjela
29818
$endgroup$
1
$begingroup$
Have you tried adapting a proof from the case where $X=mathbb C$?
$endgroup$
– Aweygan
Jan 13 at 23:51
$begingroup$
Not yet, but I think that if X is finite dimensional then the limit exists
$endgroup$
– Djalal Ounadjela
Jan 14 at 11:18
add a comment |
$begingroup$
Let $X$ be a Banach space and let $Usubsetmathbb{C}
$ be open. If we have an analytic function $f:Usetminus left{ 0right}
rightarrow X$ such that $underset{xin Usetminus left{ 0right} }{sup
}leftVert fleft( xright) rightVert <infty ,$ can we say that the
limit $underset{xrightarrow 0}{lim }fleft( xright) $ exists. Thank you !
complex-analysis functional-analysis limits continuity analytic-functions
asked Jan 13 at 23:00
Djalal OunadjelaDjalal Ounadjela
29818
$endgroup$
Let $X$ be a Banach space and let $Usubsetmathbb{C}
$ be open. If we have an analytic function $f:Usetminus left{ 0right}
rightarrow X$ such that $underset{xin Usetminus left{ 0right} }{sup
}leftVert fleft( xright) rightVert <infty ,$ can we say that the
limit $underset{xrightarrow 0}{lim }fleft( xright) $ exists. Thank you !
complex-analysis functional-analysis limits continuity analytic-functions
complex-analysis functional-analysis limits continuity analytic-functions
asked Jan 13 at 23:00
Djalal OunadjelaDjalal Ounadjela
29818
asked Jan 13 at 23:00
Djalal OunadjelaDjalal Ounadjela
29818
asked Jan 13 at 23:00
Djalal OunadjelaDjalal Ounadjela
29818
asked Jan 13 at 23:00
Djalal OunadjelaDjalal Ounadjela
29818
asked Jan 13 at 23:00
Djalal OunadjelaDjalal Ounadjela
29818
29818
1
$begingroup$
Have you tried adapting a proof from the case where $X=mathbb C$?
$endgroup$
– Aweygan
Jan 13 at 23:51
$begingroup$
Not yet, but I think that if X is finite dimensional then the limit exists
$endgroup$
– Djalal Ounadjela
Jan 14 at 11:18
add a comment |
1
$begingroup$
Have you tried adapting a proof from the case where $X=mathbb C$?
$endgroup$
– Aweygan
Jan 13 at 23:51
$begingroup$
Not yet, but I think that if X is finite dimensional then the limit exists
$endgroup$
– Djalal Ounadjela
Jan 14 at 11:18
1
1
$begingroup$
Have you tried adapting a proof from the case where $X=mathbb C$?
$endgroup$
– Aweygan
Jan 13 at 23:51
$begingroup$
Have you tried adapting a proof from the case where $X=mathbb C$?
$endgroup$
– Aweygan
Jan 13 at 23:51
$begingroup$
Not yet, but I think that if X is finite dimensional then the limit exists
$endgroup$
– Djalal Ounadjela
Jan 14 at 11:18
$begingroup$
Not yet, but I think that if X is finite dimensional then the limit exists
$endgroup$
– Djalal Ounadjela
Jan 14 at 11:18
add a comment |
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1
$begingroup$
Have you tried adapting a proof from the case where $X=mathbb C$?
$endgroup$
– Aweygan
Jan 13 at 23:51
$begingroup$
Not yet, but I think that if X is finite dimensional then the limit exists
$endgroup$
– Djalal Ounadjela
Jan 14 at 11:18