Introduction to Complex Theory of Differential Equations

• Main Authors: Savin, Anton (Author), Sternin, Boris (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Geophysics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Functions of complex variables.; Global Analysis and Analysis on Manifolds.; Partial Differential Equations.; Several Complex Variables and Analytic Spaces.; Geophysics/Geodesy.

This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires n...

Table of Contents:

• Leray residues
• Ramied integrals
• Asymptotics of ramied integrals
• Ramied Fourier transform
• Properties of ramied Fourier transform
• The Cauchy problem for equations with constant coefficients
• Singularities of the solution of Cauchy problem
• The Cauchy problem for equations with variable coefficients. Leray's uniformization
• Balayage inwards problem
• Mother body problem
• Hints for exercises.