Functional Calculus for Unbounded Operators
In the first two sections of this chapter the theory of Riesz projections and the functional calculus developed in Chapter I are extended to unbounded linear operators. This extension is quite straightforward. The next two sections concern a more difficult problem, namely, the case when the contour of integration goes through infinity. For the unbounded case (when infinity always belongs to the spectrum) the solution requires a spectral decomposition for the spectrum at infinity.
KeywordsHalf Plane Bounded Linear Operator Spectral Decomposition Finite Type Functional Calculus
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