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math.FA2025
The Kaczmarz Algorithm in Hilbert -modules
Daniel Alpay, Chad Berner, Eric S. Weber
The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the settin…
math.FA2024
Operator orbit frames and frame-like Fourier expansions
Chad Berner, Eric S. Weber
Frames in a Hilbert space that are generated by operator orbits are vastly studied because of the applications in dynamic sampling and signal recovery. We demonstrate in this paper…
math.FA2024
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…