Analytic singular support properties for integral operators in hyperfunctions (Q899106)

The authors consider integral operators whose kernels are hyperfunctions and give a result on the analytic singular support of the kernel hyperfunction. This paper is a continuation of previous work by the same authors [Adv. Math. 231, No. 3--4, 1439--1461 (2012; Zbl 1271.46035)]. The proof of the main result (Theorem 1.1) is based on the possibility of expressing a given kernel, up to a real analytic remainder, in the form \(P(D_x){\mathcal K}'\), where \(P(D_x)\) is an (infinite order) elliptic differential operator and \({\mathcal K}'\) is an ultradifferentiable function in the sense of \textit{R. W. Braun} et al. [Result. Math. 17, No. 3--4, 206--237 (1990; Zbl 0735.46022)] (Theorem 5.1).