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