A note on the functional calculus for unbounded self-adjoint operators |
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Authors: | Patrick M. Fitzpatrick |
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Affiliation: | 1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA
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Abstract: | Two theorems of Riesz and Lorch (1936) are used to pass directly from the functional calculus for bounded symmetric operators to that for unbounded self-adjoint operators, thereby considerably shortening the passage via the spectral resolution for unbounded self-adjoint operators, and making particularly transparent the manner in which properties of the functional calculus for bounded operators are inherited by those which are unbounded. |
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