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arXiv · 2108.00157

Adaptive Fourier decomposition of slice regular functions

Ming Jin·Ieng Tak Leong·Tao Qian·Guangbin Ren
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Abstract

In the slice Hardy space over the unit ball of quaternions, we introduce the slice hyperbolic backward shift operator $\mathcal S_a$ with the decomposition process $$f=e_a\langle f, e_a\rangle+B_{a}*\mathcal S_a f,$$ where $e_a$ denotes the slice normalized Szeg\"o kernel and $ B_a $ the slice Blaschke factor. Iterating the above decomposition process, a corresponding maximal selection principle gives rise to the slice adaptive Fourier decomposition. This leads to a adaptive slice Takenaka-Malmquist orthonormal system.

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Ming Jin, Ieng Tak Leong, Tao Qian, Guangbin Ren. 2021-07-31. Adaptive Fourier decomposition of slice regular functions. https://arxiv.org/abs/2108.00157

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