  Self-adjoint operators on infinite-dimensional spaces with continuous spectra
are abundant but do not possess a basis of eigenfunctions. Rather,
diagonalization is achieved through spectral measures. The SpecSolve package
[SIAM Rev., 63(3) (2021), pp. 489--524] computes spectral measures of general
(self-adjoint) differential and integral operators by combining
state-of-the-art adaptive spectral methods with an efficient resolvent-based
strategy. The algorithm achieves arbitrarily high orders of convergence in
terms of a smoothing parameter, allowing computation of both discrete and
continuous spectral components. This article extends SpecSolve to two important
classes of operators: singular integro-differential operators and general
operator pencils. Essential computational steps are performed with
off-the-shelf spectral methods, including spectral methods on the real line,
the ultraspherical spectral method, Chebyshev and Fourier spectral methods, and
the ($hp$-adaptive and sparse) ultraspherical spectral element method. This
collection illustrates the power and flexibility of SpecSolve's
"discretization-oblivious" paradigm.
