Boutet de Monvel, L. Complément sur le noyau de Bergman. (Complement to the Bergman kernel). (French) Zbl 0624.32014 Sémin. Équations Dériv. Partielles 1985-1986, Exposé no. 20, 13 p. (1986). We give a complete and reasonably explicit description of the singularity of the Bergman kernel of a strictly pseudoconvex domain \(\Omega \subset {\mathbb{C}}^ n\). This follows, using the method of the stationary phase, from the following description of the singularity of the Bergman kernel (which is a reinterpretation of a result of Kashiwara): If \(\Omega\) is defined by an inequality \(u(z,\bar z)<0\) with u real analytic, and if \(B(z,\bar z)dzd\bar z\) is the Bergman kernel, then formally \(B(x,y)\) is the kernel of the inverse of the elliptic Fourier integral operator with kernel Log\(u(x,y).\) Cited in 2 ReviewsCited in 2 Documents MSC: 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) 32T99 Pseudoconvex domains 35S99 Pseudodifferential operators and other generalizations of partial differential operators 47Gxx Integral, integro-differential, and pseudodifferential operators Keywords:singularity of the Bergman kernel; strictly pseudoconvex domain; Fourier integral operator PDFBibTeX XML Full Text: Numdam EuDML