عنوان

Complex analysis, Riemann surfaces and integrable systems /

(Number (ISBN

3030346404

(Number (ISBN

9783030346409

Erroneous ISBN

9783030346393

Title Proper

Complex analysis, Riemann surfaces and integrable systems /

General Material Designation

[Book]

First Statement of Responsibility

Sergey M. Natanzon.

Place of Publication, Distribution, etc.

Cham :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

©2019.

Specific Material Designation and Extent of Item

1 online resource (148 pages)

Series Title

Moscow Lectures ;

Volume Designation

v. 3

Text of Note

Includes bibliographical references and index.

Text of Note

Holomorphic functions -- Meromorphic functions -- Riemann's theorem -- Harmonic functions -- Riemann surfaces and their modules -- Compact Riemann surfaces and algebraic curves -- Riemann-Roch theorem and theta functions -- Integrable Systems -- The formula for the conformal mapping of an arbitrary domain into the unit disk.

0

Text of Note

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided. We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications. After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk - a classical problem that has important applications in hydrodynamics, gas dynamics, etc. The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030346409

Title

Complex Analysis, Riemann Surfaces and Integrable Systems.

International Standard Book Number

9783030346393

Functions of complex variables.

Integral equations.

Riemann surfaces.

Functions of complex variables.

Integral equations.

Riemann surfaces.

Number

Edition

Class number

Natanzon, S. M.,1948-

Date of Transaction

20200823094540.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y