A NOTE ON THE MODULUS OF CONTINUITY FOR ILL-POSED PROBLEMS IN HILBERT SPACE
A NOTE ON THE MODULUS OF CONTINUITY FOR ILL-POSED PROBLEMS IN HILBERT SPACE
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发表时间：
2012
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通讯作者：
V. Vasin
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作者：
V. Vasin
研究了Hilbert空间中的线性不适定算子方程。通过施加某些平滑假设（通常相对于控制方程的算子给出），此类方程成为有条件适定的。这通常是根据一般源条件进行的。最近的光滑性元素的分布函数的性质，这个元素的基本操作员的自伴缔合。在所有情况下，原来的不适定问题变成适定的，相应的连续模的性质是有趣的，特别是这是否是一个凹函数。推广了关于B中紧算子的一个与连续模有关的函数的已有结果。Hofmann，P. Mathé，and M. Schieck，Modulus of continuity for conditional stable ill-posed problems in Hilbert space，J. Inverse Ill-Posed Probl.16（2008），no.6，567-585，到Hilbert空间中有界算子的一般情况，以及最近引入的光滑类。献给RAS通讯员弗拉基米尔V. Vasin 70周年
The authors study linear ill-posed operator equations in Hilbert space. Such equations become conditionally well-posed by imposing certain smoothness assumptions, often given relative to the operator which governs the equation. Usually this is done in terms of general source conditions. Recently smoothness of an element was given in terms of properties of the distribution function of this element with respect to the self-adjoint associate of the underlying operator. In all cases the original ill-posed problem becomes well-posed, and properties of the corresponding modulus of continuity are of interest, specifically whether this is a concave function. The authors extend previous concavity results of a function related to the modulus of continuity, and obtained for compact operators in B. Hofmann, P. Mathé, and M. Schieck, Modulus of continuity for conditionally stable ill-posed problems in Hilbert space, J. Inverse Ill-Posed Probl. 16 (2008), no. 6, 567–585, to the general case of bounded operators in Hilbert space, and for recently introduced smoothness classes. Dedicated to the 70th anniversary of the RAS Corresponding-Member Vladimir V. Vasin