On an Open Question about the Stability of the Finite Section Method for a Class of Convolution Type Operators

Markus Seidel

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On an Open Question about the Stability of the Finite Section Method for a Class of Convolution Type Operators

机译：关于一类卷积型算子的有限截面方法的稳定性的一个开放性问题

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We clear up an open question on the characterization of the stability of operator sequences arising from the finite section method for convolution type operators with piecewise continuous and slowly oscillating generating functions. In particular, it turns out that the answer is different from what was conjectured so far and simplifies the previously known results.

机译：对于因分段连续且缓慢振荡的生成函数的卷积型算子的有限截面方法，我们对算子序列的稳定性刻画了一个开放的问题。尤其是，事实证明答案与迄今为止的推测不同，并且简化了先前已知的结果。

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来源
《Integral Equations and Operator Theory》 |2013年第2期|249-255|共7页
作者
Markus Seidel;
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作者单位

Department of Mathematics Chemnitz University of Technology">(1);

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原文格式 PDF
正文语种 eng
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关键词
convolution operators; finite section method; local invertibility;

机译：卷积运算符;有限截面法局部可逆;

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专利

1. On an Open Question about the Stability of the Finite Section Method for a Class of Convolution Type Operators [J] . Seidel M. Integral equations and operator theory . 2013,第2期

机译：关于一类卷积型算子的有限截面方法的稳定性的一个开放性问题
2. Erratum to: Finite Section Method for a Banach Algebra of Convolution Type Operators on Lp(?) with Symbols Generated by PC and SO (Integr. Equ. Oper. Theory, (2010), 67, (559-600), 10.1007/s00020-010-1784-9) [J] . Karlovich A.Y., Mascarenhas H., Santos P.A. Integral equations and operator theory . 2011,第3期

机译：勘误到：Lp（？）上具有PC和SO生成的符号的卷积型算子Banach代数的有限截面方法（Integr。Equ。Oper。Theory，（2010），67，（559-600），10.1007 / s00020 -010-1784-9）
3. Erratum to: Finite Section Method for a Banach Algebra of Convolution Type Operators on Lp(mathbbR){L^{p}(mathbb{R})} with Symbols Generated by PC and SO [J] . Alexei Yu. Karlovich, Helena Mascarenhas, Pedro A. Santos Integral Equations and Operator Theory . 2011,第3期

机译：勘误到：L p （mathbbR）{L ^ {p}（mathbb {R}）}上的卷积类型算子Banach代数的有限截面方法，其符号由PC和SO生成
4. Stability of Linear Systems with Caputo Fractional-, Variable-Order Difference Operator of Convolution Type [C] . Dorota Mozyrska, Małgorzata Wyrwas International Conference on Telecommunications and Signal Processing . 2018

机译：卷积类型的分数阶，变阶差分算子的线性系统的稳定性
5. Alternative methodology for modeling long-term stability in wellbores in reservoirs used for carbon capture and storage and experimental determination of deterioration of cement Type 10 and Class G. [D] . Condor, Jose. 2009

机译：用于碳捕集和封存的油藏中井眼长期稳定性建模的另一种方法，并通过实验确定10型和G类水泥的变质。
6. On Variation-Diminishing Integral Operators of the Convolution Type [O] . I. J. Schoenberg 1948

机译：卷积类型的变分积分算子
7. Erratum to: Finite Section Method for a Banach Algebra of Convolution Type Operators on $${L^{p}(mathbb{R})}$$ with Symbols Generated by PC and SO [O] . Alexei Yu. Karlovich, Helena Mascarenhas, Pedro A. Santos 2011

机译：错误到：在$$ {l ^ {p}（ mathbb {r}）} $$与PC生成的符号等符号，有限剖面方法
8. Evolution operator equation: Integration with algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory [R] . Dattoli, G. , Torre, A. , Ottaviani, P. L. , 1997

机译：演化算子方程：与代数和有限差分方法的集成。应用于经典和量子力学中的物理问题和量子场论

On an Open Question about the Stability of the Finite Section Method for a Class of Convolution Type Operators

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