Added some example facts.
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\begin{definition}[Hardy Space]
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\label{definition:hardy-space}
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Let $D = B_\complex(0, 1)$, then the \textbf{Hardy space} $H^\infty(D)$ is the space of all bounded holomorphic functions on $D$, equipped with the uniform norm.
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Let $D = B_\complex(0, 1)$, then the \textbf{Hardy space} $H^\infty(D)$ is the algebra of all bounded holomorphic functions on $D$, equipped with the uniform norm.
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\end{definition}
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\begin{proposition}
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