Date of Award
8-2023
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Chair/Advisor
Dr. Mishko Mitkovski
Committee Member
Dr. Shitao Liu
Committee Member
Dr. Martin Schmoll
Committee Member
Dr. Cody Stockdale
Committee Member
Dr. James Coykendall
Abstract
Let H be a reproducing kernel Hilbert space with reproducing kernel elements {Kx} indexed by a measure space {X,mu}. If H can be embedded in L2(X,mu), then H can be viewed as a framed Hilbert space. We study concentration of orthonormal sequences in such reproducing kernel Hilbert spaces.
Defining different versions of concentration, we find quantitative upper bounds on the number of orthonormal functions that can be classified by such concentrations. Examples are shown to prove sharpness of the bounds. In the cases that we can add "concentrated" orthonormal vectors indefinitely, the growth rate of doing so is shown.
Recommended Citation
Alvarez, Travis, "Concentration Theorems for Orthonormal Sequences in a Reproducing Kernel Hilbert Space" (2023). All Dissertations. 3363.
https://tigerprints.clemson.edu/all_dissertations/3363