154 citations · 368 across the 11 of their papers we have counts for
5 papers · 1 filter
Fourier series for singular measures in higher dimensions
Chad Berner, John E. Herr, Palle E. T. Jorgensen +1
For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal Fourier expansions. Our results hold for probability measures with f…
A Characterization of Boundary Representations of Positive Matrices in the Hardy Space via the Abel Product
John E. Herr, Palle E. T. Jorgensen, Eric S. Weber
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider i…
A matrix characterization of boundary representations of positive matrices in the Hardy space
John E. Herr, Palle E. T. Jorgensen, Eric S. Weber
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider i…
Positive Matrices in the Hardy Space with Prescribed Boundary Representations via the Kaczmarz Algorithm
John E. Herr, Palle E. T. Jorgensen, Eric S. Weber
For a singular probability measure on the circle, we show the existence of positive matrices on the unit disc which admit a boundary representation on the unit circle with resp…
Fourier Series for Singular Measures
John E. Herr, Eric S. Weber
Using the Kaczmarz algorithm, we prove that for any singular Borel probability measure on , every possesses a Fourier series of the form $f(x)=\sum_{n=0}^{…