An open problem in complex analytic geometry arising in harmonic analysis

Abstract

In this paper, an open problem in the multidimensional complex analysis is presented that arises in the harmonic analysis related to the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential equations. The problem is discussed in a self-contained elementary way and some results towards its resolution are presented. A conjecture concerning the structure of appearing affine fibrations is formulated. © 2013 EDP Sciences.