LikeMath
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Hi,
Let [itex]H^2[/itex] be the Hardy space on the open unit disk.
I am wondering how can I compute the following inner product
[itex]<\frac{1}{\left(1-\overline{\alpha_1} z\right)^2}\frac{z-\alpha_2}{1-\overline{\alpha_2} z},\frac{z}{\left(1-\overline{\alpha_1} z\right)^2}>,[/itex]
where [itex]\alpha_1,\alpha_2[/itex] in the unit disk.
I tried to expand the functions but it became complicated. Also it did not work with the integration.
Is there an idea to be tried?
Thanks in advanced
Likemath
Let [itex]H^2[/itex] be the Hardy space on the open unit disk.
I am wondering how can I compute the following inner product
[itex]<\frac{1}{\left(1-\overline{\alpha_1} z\right)^2}\frac{z-\alpha_2}{1-\overline{\alpha_2} z},\frac{z}{\left(1-\overline{\alpha_1} z\right)^2}>,[/itex]
where [itex]\alpha_1,\alpha_2[/itex] in the unit disk.
I tried to expand the functions but it became complicated. Also it did not work with the integration.
Is there an idea to be tried?
Thanks in advanced
Likemath