  Phase-space distributions are widely applied in quantum optics to access the
nonclassical features of radiations fields. In particular, the inability to
interpret the Glauber-Sudarshan distribution in terms of a classical
probability density is the fundamental benchmark for quantum light. However,
this phase-space distribution cannot be directly reconstructed for arbitrary
states, because of its singular behavior. In this work, we perform a
characterization of the Glauber-Sudarshan representation in terms of
distribution theory. We address important features of such distributions: (i)
the maximal degree of their singularities is studied, (ii) the ambiguity of
representation is shown, and (iii) their dual space for nonclassicality tests
is specified. In this view, we reconsider the methods for regularizing the
Glauber-Sudarshan distribution for verifying its nonclassicality. This
treatment is supported with comprehensive examples and counterexamples.
