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Let [itex]S[/itex] denote the shift operator on the Hardy space on the unit disc [itex]H^2[/itex], that is [itex](Sf)(z)=zf(z)[/itex].

My question is to show the following identity

[itex](1-\lambda S^*)^{-1}S^*f (z)=\frac{f(z)-f(\lambda)}{z-\lambda},[/itex]

where [itex]\lambda,z\in\mathbb{D}[/itex]

Thanks in advance

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# Inverse of the adjoint of the shift operator

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