Topics in Several Complex Variables.

Cover -- Title page -- Contents -- Preface -- Polynomials on parabolic manifolds -- 1. Introduction -- 2. Parabolic manifolds -- 3. Aspects of pluripotential theory on -parabolic manifolds -- 4. Example -- 5. Regular parabolic manifolds -- References -- Pseudoholomorphic discs and symplectic structures in Hilbert space -- 1. Introduction -- 2. Almost complex structures on Hilbert spaces -- 3. Some properties of the Cauchy integral -- 4. Local existence and regularity of pseudoholomorphic discs -- 5. Boundary value problems for -holomorphic discs -- 6. Non-squeezing for symplectic transformations -- 7. Appendix I: Morrey's embedding -- 8. Appendix II: Proof of Theorem 3.2 -- References -- Pluripolarity of graphs of quasianalytic functions of several complex variables -- 1. Introduction -- 2. Preliminaries -- 3. Pluripolarity of graphs of Gonchar quasianalytic functions of several variables -- 4. Pluripolarity of graphs of algebroid functions -- 5. Pluripolarity of graphs of Denjoy quasianalytic functions of several variables -- References -- Lagrangian inclusion with an open Whitney umbrella is rationally convex -- 1. Introduction -- 2. Proof of Theorem 1 -- References -- On systems of non-algebraic equations in ℂⁿ -- Introduction -- 1. Preliminaries -- 2. Calculation of residue integrals -- 3. Power sums -- 4. Finding the sums of some multivariate series -- References -- Integral formulas for some matrix domains -- 1. Introduction -- 2. Results -- 3. Open problems -- References -- Nevanlinna's characteristic functions with complex Hessian potential -- 1. Introduction -- 2. - ℎ functions -- 3. Properties of the order function -- 4. Upper bounds for -order functions -- References -- Holomorphic continuation of functions in the domains with singular boundaries -- References -- Segre varieties and uniform estimates for harmonic functions.

1. Introduction -- 2. Uniform estimates for harmonic functions -- 3. Proof of Theorem 1 -- References -- Uniqueness property for Gonchar quasianalytic functions of several variables -- 1. Introduction -- 2. Main result -- 3. A theorem of Plesniak -- Acknowledgement -- References -- Capacity dimension of the Perez-Marco set -- 1. Introduction -- 2. Main result -- References -- Analogue of the Lelong's theorem for - ℎ functions -- Introduction -- 1. - ℎ functions and their properties -- 2. A criteria of pluriharmonicity -- References -- Pluriregular compacts in ℙⁿ -- Introduction -- 1. Quasiplurisubharmonic functions -- 2. Green function and pluriregularity in ℙⁿ -- 3. Appendix. Pluriregularity of the Julia set -- References -- Back Cover.

This volume contains the proceedings of the Special Session on Several Complex Variables, which was held during the first USA-Uzbekistan Conference on Analysis and Mathematical Physics from May 20-23, 2014, at California State University, Fullerton. This volume covers a wide variety of topics in pluripotential theory, symplectic geometry and almost complex structures, integral formulas, holomorphic extension, and complex dynamics. In particular, the reader will find articles on Lagrangian submanifolds and rational convexity, multidimensional residues, S-parabolic Stein manifolds, Segre varieties, and the theory of quasianalytic functions.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.