Interpolation inequalities for modified Sobolev spaces and their implications to inversion of Radon transform

被引：0
|
作者：
Nair, M. Thamban [1 ]
Boggarapu, Pradeep [1 ]
机构：
[1] BITS Pilani KK Birla Goa Campus, Dept Math, Sancoale, Goa, India
来源：
PROCEEDINGS OF THE INDIAN NATIONAL SCIENCE ACADEMY | 2023年 / 89卷 / 02期
关键词：
Radon trasform; Ill-posed; Modified sobolev spaces; Interpolation inequality; Worst case error;
D O I：
10.1007/s43538-023-00164-y
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The implications of interpolation inequality for Hilbert scales for obtaining estimates for the worst case error for ill-posed problems are well known. In this paper, we prove interpolation inequalities for the modified Sobolev scales, the general form of which was introduced by Sharafutdinov (Inverse Problems 33:025002, 2017), and make use of them along with the recently obtained modified Reshetnyak formulas for Radon transform to obtain error estimates for the worst case error associated with the Radon transform and appropriate source sets.
引用
收藏
页码：410 / 415
页数：6
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