Quadratic forms of skew-normal random vectors

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On fundamental skew distributions (2005, background): “[15] derive the moments of random vectors with multivariateSNdistributions and their quadratic forms (see also [24]).”
The Skew‐normal Distribution and Related Multivariate Families * (2005, background): “Additional distributional properties can be found in Loperfido (2001) and Genton et al. (2001).”
Characterization of the skew-normal distribution (2004, background): “Loperfido (2001), Genton et al. (2001) and Gupta and Huang (2002) focused on probabilistic properties of quadratic skew-normal variates.”
A SKEW-SYMMETRIC REPRESENTATION OF MULTIVARIATE DISTRIBUTIONS (2002, unknown): “This has important implications for statistical inference based on quadratic forms as noted by Genton, He and Liu (2001) and Loperfido (2001).”
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution (2003, background): “This set of results includes propositions 7–9 of Azzalini and Capitanio (1999) and propositions 1, 2 and 6 (parts 1 and 3) of Loperfido (2001).”
Generalized skew-Cauchy distribution ☆ (2007, background): “Quadratic forms of skew-normal random vectors have been studied by Azzalini (1985), Azzalini and Dalla Valle (1996), Azzalini and Capitanio (1999), Loperfido (2001), Genton et al. (2001), and Gupta and Huang (2002).”