Harmonic Approximation
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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, Ra...
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.
Table of contents:
1. Review of thin sets; 2. Approximation on compact sets; 3. Fusion of harmonic functions; 4. Approximation on relatively closed sets; 5. Carleman approximation; 6. Tangential approximation at infinity; 7. Subharmonic extension and approximation; 8. The Dirichlet problem with non-compact boundary; 9. Further applications.
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. Throughout, inspiration is drawn from holomorphic results such as the well-known theorems of Runge and Mergelyan. This book is aimed at graduate students and researchers who have some knowledge of subharmonic functions, or an interest in holomorphic approximation.
This book is aimed at graduate students and researchers who have some knowledge of subharmonic functions, or an interest in holomorphic approximation.
Table of contents:
1. Review of thin sets; 2. Approximation on compact sets; 3. Fusion of harmonic functions; 4. Approximation on relatively closed sets; 5. Carleman approximation; 6. Tangential approximation at infinity; 7. Subharmonic extension and approximation; 8. The Dirichlet problem with non-compact boundary; 9. Further applications.
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. Throughout, inspiration is drawn from holomorphic results such as the well-known theorems of Runge and Mergelyan. This book is aimed at graduate students and researchers who have some knowledge of subharmonic functions, or an interest in holomorphic approximation.
This book is aimed at graduate students and researchers who have some knowledge of subharmonic functions, or an interest in holomorphic approximation.
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