Application of Holomorphic Functions in Two and Higher Dimensions

• Main Authors: Gürlebeck, Klaus (Author), Habetha, Klaus (Author), Sprößig, Wolfgang (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2016.
• Subjects: Mathematics.; Functional analysis.; Functions of complex variables.; Integral transforms.; Operational calculus.; Partial differential equations.; Integral Transforms, Operational Calculus.; Functions of a Complex Variable.; Partial Differential Equations.; Functional Analysis.

This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Cli...

Table of Contents:

• 1.Basic Properties of Holomorphic Functions
• 2.Conformal and Quasi-conformal Mappings
• 3.Function Theoretic Function spaces
• 4.Operator Calculus
• 5.Decompositions
• 6.Some First Order Systems of Partial Differential Equations
• 7.Boundary Value Problems of Second Order Partial Differential Equations
• 8.Some Initial-boundary Value Problems
• 9.Riemann-Hilbert Problems
• 10.Initial Boundary Value Problems on the Sphere
• 11.Fourier Transforms
• Bibliography
• Index.