I'm looking for a certain kind of approach to quantum mechanics. In most places I've looked, almost all of the exposition on how to employ construct observables in quantum mechanics is that of compact self-adjoint operators. This goes hand in hand with the fact that the separable Hilbert space will have a countable basis, which can be chosen to be set of eigenvectors of such an operator. What I find a little hard to follow and to integrate in all this theory is the subsequent treament of unbounded self-adjoint operators, which is usually also rather short in comparison with the latter, because there is little mathematical care in making things clear, with the distributional character of the "eigenstates" and these operators, for example, typically just appealing to intuition and some vague notion of "continuous basis states".
In that vein, I'm looking for a book that presents observables, both with discrete and continuous spectra, in a united front, so that both unbounded and compact self-adjoint operators can be understood as specific instances of that theory. In lieu of an example, take this lecture series on Youtube. This is more like what I was looking for, but I am not exactly happy with the whole projection valued measures deal, since it is not common to be found in the literature, and so I am having a hard time "translating" "PVM talk" into "canonical talk" and notation.