Oversmooting Tikhonov regularization in Banach spaces
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Speaker: CHEN Dehan (Central China Normal University)
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Time: Dec 8, 2020, 15:00-16:00
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Location: Tencent Meeting ID 140 142 882
Abstract: This talk 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 l1, Bessel potential spaces, and Besov spaces are discussed.
