论文标题
在Banach空间中过度厚度的Tikhonov正规化
Oversmoothing Tikhonov regularization in Banach spaces
论文作者
论文摘要
本文为Banach空间中非线性不良的操作员方程式开发了Tikhonov正则化理论。作为主要挑战，我们考虑了所谓的超平滑状态，因为Tikhonov惩罚无法捕获真正的解决方案规律性并导致解决方案中的无限罚款价值。我们通过使用霍明型功能积分的可逆部门操作员和巴拉赫空间中插值尺度的突出理论来建立希尔伯特融合理论的广泛扩展。讨论了涉及$ \ ell^1 $，贝塞尔潜在空间和贝斯托空间的拟议理论的应用。
This paper develops a Tikhonov regularization theory for nonlinear ill-posed operator equations in Banach spaces. As the main challenge, we consider the so-called oversmoothing state in the sense that the Tikhonov penalization is not able to capture the true solution regularity and leads to the infinite penalty value in the solution. We establish a vast extension of the Hilbertian convergence theory through the use of invertible sectorial operators from the holomorphic functional calculus and the prominent theory of interpolation scales in Banach spaces. Applications of the proposed theory involving $\ell^1$, Bessel potential spaces, and Besov spaces are discussed.
