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Holomorphic Functions and Integral Representations in Several Complex Variab...
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Holomorphic Functions and Integral Representations in Several Complex Variab...

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    Item specifics

    Condition
    Good: A book that has been read but is in good condition. Very minimal damage to the cover including ...
    Release Year
    1986
    Book Title
    Holomorphic Functions and Integral Representations in Several ...
    ISBN
    9780387962597

    About this product

    Product Identifiers

    Publisher
    Springer New York
    ISBN-10
    038796259X
    ISBN-13
    9780387962597
    eBay Product ID (ePID)
    14038282857

    Product Key Features

    Number of Pages
    Xx, 392 Pages
    Publication Name
    Holomorphic Functions and Integral Representations in Several Complex Variables
    Language
    English
    Publication Year
    1986
    Subject
    Functional Analysis, Mathematical Analysis, Complex Analysis
    Type
    Textbook
    Author
    R. Michael Range
    Subject Area
    Mathematics
    Series
    Graduate Texts in Mathematics Ser.
    Format
    Hardcover

    Dimensions

    Item Weight
    58.9 Oz
    Item Length
    9.2 in
    Item Width
    6.1 in

    Additional Product Features

    Intended Audience
    Scholarly & Professional
    LCCN
    85-030309
    Dewey Edition
    22
    Series Volume Number
    108
    Number of Volumes
    1 vol.
    Illustrated
    Yes
    Dewey Decimal
    515.98
    Table Of Content
    I Elementary Local Properties of Holomorphic Functions.- II Domains of Holomorphy and Pseudoconvexity.- III Differential Forms and Hermitian Geometry.- IV Integral Representations in ?n.- V The Levi Problem and the Solution of ? on Strictly Pseudoconvex Domains.- VI Function Theory on Domains of Holomorphy in ?n.- VII Topics in Function Theory on Strictly Pseudoconvex Domains.- Appendix A.- Appendix B.- Appendix C.- Glossary of Symbols and Notations.
    Synopsis
    The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu­ lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ­ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com­ plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods., This is an introductory text in several complex variables, using methods of integral representations. It begins with elementary local results, discusses basic new concepts of the multi-dimensional theory such as pseudoconvexity and holomorphic convexity, and leads up to complete proofs of fundamental global results, both classical and new., The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu- lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ- ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com- plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
    LC Classification Number
    QA299.6-433

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