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:A function <math>h:D\rightarrow Y</math> is holomorphic if it is locally bounded and if for each <math>x\in D</math>, <math>y\in X</math> and linear functional <math>\ell\in Y^{\ast}</math>, the function <math>f(\lambda)=\ell (h(x+\lambda y))</math> is holomorphic at <math>\lambda=0</math>.
Since it says ''[[Infinite-dimensional holomorphy#Vector-valued holomorphic functions defined in the complex plane|useful criterion]]'', the holomorphic on this page may mean a weak holomorphic. I've read that the reason why holomorphy has a stronger meaning than real variables is that it has an unlimited approach to holomorphic points compared to real numbers. I may need to add a description of the <math>C^n</math> space to make the space we are Integrate more clear. I try read it again without knowing it. Thanks!--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 13:39, 15 December 2020 (UTC)
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