Footnote:
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Description:
The objective of this survey is to collect and elaborate on different tools, both well-established and more recent ones, which have been developed in the last decades to investigate spectral properties of non-self-adjoint operators of the form $H = H_0 + V$. More specifically, we will show how Hardy-type and Sobolev inequalities, together with Virial theorems and Birman-Schwinger principles enter into play in the analysis of the spectrum of these Hamiltonians.