Quaternionic slice hyperbolic backward shift operators and adaptive greedy algorithm


Abstract in English

In the slice Hardy space over the unit ball of quaternions, we introduce the slice hyperbolic backward shift operators $mathcal S_a$ based on the identity $$f=e_alangle f, e_arangle+B_{a}*mathcal S_a f,$$ where $e_a$ denotes the slice normalized Szego kernel and $ B_a $ the slice Mobius transformation. By iterating the identity above, the greedy algorithm gives rise to the slice adaptive Fourier decomposition via maximum selection principle. This leads to the slice Takenaka-Malmquist orthonormal system.

Download