齐次函数：新的特性和应用

IF 0.3 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute Pub Date : 2017-08-01 DOI:10.1016/j.trmi.2016.12.006

Moncef Elghribi , Hakeem A. Othman , Al-Hossain Ahmed Al-Nashri

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引用次数: 5

摘要

利用量子微积分，用Jackson导数代替经典导数算子，对负次R上的正齐次函数进行了新的对应物欧拉齐次函数定理的刻画。作为应用，我们首先描述与杰克逊导数相关的谐波函数。然后，给出了与欧拉算子类似的Cauchy问题的解。利用这个解，我们研究了相关的ν-势。讨论了其马尔可夫性。

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Homogeneous functions: New characterization and applications

Positive homogeneous functions on $R$ of a negative degree are characterized by a new counterpart of the Euler’s homogeneous function theorem using quantum calculus and replacing the classical derivative operator by Jackson derivative. As application we start by characterizing the harmonic functions associated to Jackson derivative. Then, the solution of the Cauchy problem associated to the analogue of the Euler operator is given. Using this solution we study the associated $ν$ -potential. Its Markovianity property is treated.

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来源期刊

Transactions of A Razmadze Mathematical Institute MATHEMATICS-

CiteScore

0.50

自引率

50.00%

发文量

审稿时长

22 weeks