Abstract
This chapter focuses on the special properties of positive harmonic functions. We will describe the positive harmonic functions defined on all of R n (Liouville’s Theorem), show that positive harmonic functions cannot oscillate wildly (Harnack’s Inequality), and characterize the behavior of positive harmonic functions near isolated singularities (Bôcher’s Theorem).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Axler, S., Bourdon, P., Ramey, W. (2001). Positive Harmonic Functions. In: Harmonic Function Theory. Graduate Texts in Mathematics, vol 137. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-8137-3_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-8137-3_3
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