Abstract
The Kelvin transform performs a role in harmonic function theory analogous to that played by the transformation f(z) ↦ f(1/z) in holomorphic function theory. For example, it transforms a function harmonic inside the unit sphere into a function harmonic outside the sphere. In this chapter, we introduce the Kelvin transform and use it to solve the Dirichlet problem for the exterior of the unit sphere and to obtain a reflection principle for harmonic functions. Later, we will use the Kelvin transform in the study of isolated singularities of harmonic functions.
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© 2001 Springer Science+Business Media New York
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Axler, S., Bourdon, P., Ramey, W. (2001). The Kelvin Transform. In: Harmonic Function Theory. Graduate Texts in Mathematics, vol 137. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-8137-3_4
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DOI: https://doi.org/10.1007/978-1-4757-8137-3_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2911-2
Online ISBN: 978-1-4757-8137-3
eBook Packages: Springer Book Archive