Holomorphic Functions and Integral Representations in Several Complex Variables - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Holomorphic Functions and Integral Representations in Several Complex Variables write by R. Michael Range. This book was released on 2013-03-09. Holomorphic Functions and Integral Representations in Several Complex Variables available in PDF, EPUB and Kindle. 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.
Integral Representation and the Computation of Combinatorial Sums
Integral Representation and the Computation of Combinatorial Sums - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integral Representation and the Computation of Combinatorial Sums write by G. P. Egorychev. This book was released on 1984-12-31. Integral Representation and the Computation of Combinatorial Sums available in PDF, EPUB and Kindle. This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics. It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating functions); these arise in practice in combinatorial analysis, the theory of algorithms and programming on a computer, probability theory, group theory, and function theory, as well as in physics and other areas of knowledge. A general approach is presented for computing sums and other expressions in closed form by reducing them to one-dimensional and multiple integrals, most often to contour integrals.
Integral Representation Theory
Integral Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integral Representation Theory write by Jaroslav Lukeš. This book was released on 2010. Integral Representation Theory available in PDF, EPUB and Kindle. This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications
Integral Representation
Integral Representation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integral Representation write by Walter Roth. This book was released on 2023-10-02. Integral Representation available in PDF, EPUB and Kindle.
Multidimensional Integral Representations
Multidimensional Integral Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Integral Representations write by Alexander M. Kytmanov. This book was released on 2015-09-09. Multidimensional Integral Representations available in PDF, EPUB and Kindle. The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappiè, Koppelman, multidimensional logarithmic residue etc., and their boundary properties. The applications considered are problems of analytic continuation of functions from the boundary of a bounded domain in C^n. In contrast to the well-known Hartogs-Bochner theorem, this book investigates functions with the one-dimensional property of holomorphic extension along complex lines, and includes the problems of receiving multidimensional boundary analogs of the Morera theorem. This book is a valuable resource for specialists in complex analysis, theoretical physics, as well as graduate and postgraduate students with an understanding of standard university courses in complex, real and functional analysis, as well as algebra and geometry.
