Holomorphic Functional Calculus

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.

Other articles related to "holomorphic functional calculus, holomorphic":

Jordan Normal Form - Generalizations - Compact Operators - Holomorphic Functional Calculus
... For more details on this topic, see holomorphic functional calculus ... The holomorphic functional calculus is defined as follows Fix a bounded operator T ... Consider the family Hol(T) of complex functions that is holomorphic on some open set G containing σ(T) ...
Holomorphic Functional Calculus - Related Results - Unbounded Operators
... A holomorphic functional calculus can be defined in a similar fashion for unbounded closed operators with non-empty resolvent set ...

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