functional calculus การใช้

• The continuous, or just the holomorphic functional calculus suffices.
• For the continuous functional calculus, the key ingredients are the following:
• This property will be used in subsequent arguments for the functional calculus.
• By property 3 of the functional calculus, the operator
• This definition can be generalized to include continuous functions using continuous functional calculus.
• The well-definedness of functional calculus now follows as an easy consequence.
• Thus a more general functional calculus is needed.
• First pass from polynomial to continuous functional calculus by using the Stone-Weierstrass theorem.
• Is positive, where the continuous functional calculus is used to define the square root.
• Property 2 and the continuous functional calculus ensure that ? preserves the *-operation.
• This is the continuous functional calculus.
• The spectral measures can be used to extend the continuous functional calculus to bounded Borel functions.
• I might take a closer look at things related to Matrix exponential and Holomorphic functional calculus.
• The compact case, described here, is a particularly simple instance of this functional calculus.
• The assumption will be applied in its entirety in showing the homomorphism property of the functional calculus.
• I know next to nothing about continuous functional calculus and that article isn't very helpful.
• In general, one uses the Borel functional calculus to calculate a non-polynomial function such as.
• For example, by properties of the Borel functional calculus, we see that for any unitary operator,
• See below for their application to compact operators, and in holomorphic functional calculus for a more general discussion.
• In this context the extension of holomorphic functions of a complex variable is developed as the holomorphic functional calculus.