Richard Basener - IBM
Boundaries for Spaces of Functions
A real linear function on an interval always takes its maximum value at one or the other (or both) of the end points. Similarly, the modulus of a complex analytic function defined on a neighborhood of the closed unit disk (modulus of z less than or equal to 1) always assumes its maximum value somewhere on the boundary of the disk (modulus of z equal to 1). These observations have given rise to a number of different useful definitions for the "boundary" of a space of functions. In this talk we will give a little history of some of these ideas, and end with a few open questions about some of these boundaries.
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