正交样条线序列的唯一性定理

IF 0.6 3区数学 Q3 MATHEMATICS Acta Mathematica Hungarica Pub Date : 2024-10-13 DOI:10.1007/s10474-024-01472-5

K. A. Keryan, A. L. Khachatryan

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引用次数: 0

摘要

如果正交样条曲线数列的部分和在度量上收敛于一个函数，并且部分和的大数满足一些必要条件，那么我们就可以通过其和得到正交样条曲线数列系数的恢复公式，前提是样条曲线系统对应于一个 "正则 "序列。此外，还证明了序列的正则性是至关重要的。

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A uniqueness theorem for orthonormal spline series

We obtain recovery formulas for coefficients of orthonormal spline series by means of its sum, if the partial sums of an orthonormal spline series converge in measure to a function and the majorant of partial sums satisfies some necessary condition, provided that the spline system corresponds to a “regular” sequence. Additionally, it is proved that the regularity of the sequence is essential.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.