Blowing-up coefficients of entire series and two theorems of Gabrielov
In the classical Weierstrass Preparation Theorem (either complex or real) the set of ``good'' directions is dense in the projective space, but it is quite possible not to find a good direction in \(0\times \mathbb{C}^k\) \((0\times \mathbb{R}^k)\). However, sometimes this would be most useful. The authors give a remedy to it, via desingularization (Theorem 2.1 and Corollary 2.4). As an application, short proofs of Gabrielov's theorems [\textit{A. M. Gabrielov}, Funct. Anal. Appl. 2, 282-291 (1968); translation from Funkts. Anal. Prilozh. 2, No. 4, 18-30 (1968; Zbl 0179.08503)], namely the theorems from his pioneer work about subanalytic sets, are given.
scientific article; zbMATH DE number 1002957
scientific article