λ平移代数中与λ-Stirling数相关的正规序

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0250

Taekyun Kim, Dae San Kim, H. Kim

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引用次数: 0

摘要

已知第二类Stirling数与Weyl代数中的正序有关，而第一类无符号Stirling数与移位代数中的正序有关。最近，Kim-Kim引入了第一类无符号斯特林数和第一类r r -斯特林数的λ \ λ -类比。在本文中，我们介绍了移位代数的λ \ λ -模拟(称为λ \ λ -移位代数)，并研究了λ \ λ -移位代数中的正常排序。从λ \平移代数的正规序出发，导出了第一类无符号斯特林数的λ \近似的恒等式。

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Normal ordering associated with λ-Stirling numbers in λ-shift algebra

Abstract It is known that the Stirling numbers of the second kind are related to normal ordering in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra. Recently, Kim-Kim introduced a λ \lambda -analogue of the unsigned Stirling numbers of the first kind and that of the r r -Stirling numbers of the first kind. In this article, we introduce a λ \lambda -analogue of the shift algebra (called λ \lambda -shift algebra) and investigate normal ordering in the λ \lambda -shift algebra. From the normal ordering in the λ \lambda -shift algebra, we derive some identities about the λ \lambda -analogue of the unsigned Stirling numbers of the first kind.

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来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.