An h^∞ space, also known as the space of bounded analytic functions, is a specific type of functional space that consists of all analytic functions on the open unit disk whose supremum norm is bounded. These functions are crucial in control theory and signal processing because they can be used to represent systems with bounded input-output characteristics. The h^∞ space is a complete normed space, making it a Banach space, which highlights its importance in the study of normed spaces and functional analysis.
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