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Arts & Sciences Electronic Theses and Dissertations
Berezin transform, Constrained subalgebras, Inner functions, Optimal polynomial approximants, Reproducing kernel spaces, Spectrum
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Some Problems In Reproducing Kernel Spaces, Christopher Felder
Some Problems In Reproducing Kernel Spaces, Christopher Felder
Arts & Sciences Electronic Theses and Dissertations
The two chapters of this thesis are comprised of work in the setting of reproducing kernel (Hilbert) spaces. These are Banach (or Hilbert) spaces of functions defined on some set, with the special property that point evaluation, on the underlying set, is bounded.
The first chapter deals with the study of inner functions. These functions have a rich history in function and operator theory in the Hardy spaces of the unit disk. The first section of this chapter studies the relationship between generalized inner functions and optimal polynomial approximants. The second section, which is joint work with Trieu Le, deals …