| 11. | This is the continuous functional calculus.
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| 12. | The spectral measures can be used to extend the continuous functional calculus to bounded Borel functions.
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| 13. | I might take a closer look at things related to Matrix exponential and Holomorphic functional calculus.
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| 14. | The compact case, described here, is a particularly simple instance of this functional calculus.
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| 15. | The assumption will be applied in its entirety in showing the homomorphism property of the functional calculus.
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| 16. | I know next to nothing about continuous functional calculus and that article isn't very helpful.
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| 17. | In general, one uses the Borel functional calculus to calculate a non-polynomial function such as.
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| 18. | For example, by properties of the Borel functional calculus, we see that for any unitary operator,
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| 19. | See below for their application to compact operators, and in holomorphic functional calculus for a more general discussion.
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| 20. | In this context the extension of holomorphic functions of a complex variable is developed as the holomorphic functional calculus.
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