Richard Basener - IBM
Notions of Boundaries for Spaces of Functions
We will begin this talk by recalling briefly why harmonic and complex analytic functions obey a maximum principle. The maximum principle leads directly to the usual notion of a "boundary" for a space of functions. We will introduce two new alternative notions of "boundary," deriving some results about these different boundaries and giving simple examples. Along the way we will derive a new proof of a theorem of Tonev. We will finish with some open questions about these boundaries.
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