In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function ƒ of a complex argument z and an operator T, the aim is to construct an operator
which in a sense extends the function ƒ from complex argument to operator argument.
This article will discuss the case where T is a bounded linear operator on some Banach space. In particular, T can be a square matrix with complex entries, a case which will be used to illustrate functional calculus and provide some heuristic insights for the assumptions involved in the general construction.
Read more about Holomorphic Functional Calculus: Functional Calculus For A Bounded Operator, Spectral Considerations, Related Results
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