Topics in several complex variables : First USA-Uzbekistan Conference, Analysis and Mathematical Physics, May 20-23, 2014, California State University, Fullerton, CA / Zair Ibragimov [and three others], editors.

Format:

Book

Contributor:

Ibragimov, Zair, editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 662

Contemporary mathematics, 662 0271-4132

Language:

English

Subjects (All):

Functions of several complex variables--Congresses.

Functions of several complex variables.

Physical Description:

1 online resource (168 pages) : illustration.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2016]

Summary:

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.

Contents:

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

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

Pluripolarity of graphs of quasianalytic functions of several complex variables

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

Lagrangian inclusion with an open Whitney umbrella is rationally convex

2. Proof of Theorem 1

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

Integral formulas for some matrix domains

2. Results

3. Open problems

Nevanlinna's characteristic functions with complex Hessian potential

2. - ℎ functions

3. Properties of the order function

4. Upper bounds for -order functions

Holomorphic continuation of functions in the domains with singular boundaries

Segre varieties and uniform estimates for harmonic functions.

1. Introduction

2. Uniform estimates for harmonic functions

3. Proof of Theorem 1

Uniqueness property for Gonchar quasianalytic functions of several variables

2. Main result

3. A theorem of Plesniak

Acknowledgement

Capacity dimension of the Perez-Marco set

Analogue of the Lelong's theorem for - ℎ functions

1. - ℎ functions and their properties

2. A criteria of pluriharmonicity

Pluriregular compacts in ℙⁿ

1. Quasiplurisubharmonic functions

2. Green function and pluriregularity in ℙⁿ

3. Appendix. Pluriregularity of the Julia set

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1927-0