Abstract
The aim of this chapter is to describe what a (closed) linear operator is. It also aims at drawing the attention of the Reader to the domain of such an operator. Such domains will be explicitly described (such as the domain of the Dirichlet Laplacian).
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Notes
- 1.
Note, however, that there is a non-self-adjoint Quantum Mechanics, related to dissipative systems.
- 2.
See Section 1.2, or prove this inequality first for \(u\in \mathscr {C}^{\infty }_0(I)\) and extend it by density.
- 3.
This means that \(\overline{\omega }\) is compact and \(\overline{\omega }\subset \Omega \).
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Cheverry, C., Raymond, N. (2021). UNBOUNDED OPERATORS. In: A Guide to Spectral Theory. Birkhäuser Advanced Texts Basler Lehrbücher. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-67462-5_2
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DOI: https://doi.org/10.1007/978-3-030-67462-5_2
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