Date of Award
Doctor of Philosophy
Eric S. Weber
Using the Kaczmarz algorithm, we obtain a Fourier series formulation for functions in the L2 space of singular measures on the unit circle. This formula is applied to the problem of finding reproducing kernel Hilbert spaces inside the classical Hardy space, where the norm is instead that of boundary integration with respect to a singular measure. We also give some conditions ensuring that these subspaces bear some essential semblances to the classical Hardy space.
John Edward Herr
Herr, John Edward, "Fourier series for singular measures and the Kaczmarz algorithm" (2016). Graduate Theses and Dissertations. 14978.