Abstract
This chapter gives statements and proofs of the spectral theorem for unbounded self-adjoint operators, in the same forms as in the bounded case, in terms of projection-valued measures, in terms of direct integrals, and in terms of multiplication operators.
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References
S.J. Bernau, The spectral theorem for unbounded normal operators. Pacific J. Math. 19, 391–406 (1966)
W. Rudin, Functional Analysis, 2nd edn. International Series in Pure and Applied Mathematics (McGraw-Hill, New York, 1991)
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Hall, B.C. (2013). The Spectral Theorem for Unbounded Self-Adjoint Operators. In: Quantum Theory for Mathematicians. Graduate Texts in Mathematics, vol 267. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7116-5_10
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DOI: https://doi.org/10.1007/978-1-4614-7116-5_10
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-7115-8
Online ISBN: 978-1-4614-7116-5
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