By Takeo Ohsawa

ISBN-10: 4431557466

ISBN-13: 9784431557463

ISBN-10: 4431562966

ISBN-13: 9784431562962

The goal of this monograph is to give the present prestige of a quickly constructing a part of numerous complicated variables, influenced by way of the applicability of potent effects to algebraic geometry and differential geometry. Highlighted are the hot special effects at the *L*² extension of holomorphic functions.

In bankruptcy 1, the classical questions of a number of advanced variables motivating the improvement of this box are reviewed after priceless arrangements from the elemental notions of these variables and of advanced manifolds akin to holomorphic services, pseudoconvexity, differential varieties, and cohomology. In bankruptcy 2, the *L*² approach to fixing the d-bar equation is gifted emphasizing its differential geometric point. In bankruptcy three, a refinement of the Oka–Cartan concept is given via this system. The *L*² extension theorem with an optimum consistent is integrated, got lately by means of Z. Błocki and by way of Q.-A. Guan and X.-Y. Zhou individually. In bankruptcy four, a number of effects at the Bergman kernel are offered, together with fresh works of Maitani–Yamaguchi, Berndtsson, and Guan–Zhou. every one of these effects are got by means of the *L*² technique. within the final bankruptcy, quite particular effects are mentioned at the lifestyles and category of convinced holomorphic foliations and Levi flat hypersurfaces as their stables units. those also are functions of the *L*² procedure acquired in the course of those 15 years.