Harmonic approximation
By: Stephen J. Gardiner.
Series: London Mathematical Society lecture note series ;; 221
Publisher: Cambridge University Press
Published: 1995
Place of publication: Cambridge; New York, NY, USA
Language: eng
Number of pages: 132
Subjects: Harmonic analysis.; Approximation theory.
Description: The subject of 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. All the time inspiration is drawn 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 the construction of pathological harmonic functions. This book is aimed at graduate students and researchers who have some knowledge of subharmonic functions, or an interest in holomorphic approximation.
Notes: Includes bibliographical references (p. [125]-129) and index.