Harmonic approximation has recently matured into a coherent research area with extensive applications. This is the first book to give a systematic account of these developments, beginning with classical results concerning uniform approximation on compact sets, and progressing through fusion techniques to deal with approximation on unbounded sets. The author draws inspiration from holomorphic results such as the well-known theorems of Runge and Mergelyan. The final two chapters deal with wide ranging and surprising applications to the Dirichlet problem, maximum principle, Radon transform and...

From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises. The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine...

From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises. The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine...