Some results for conjugate equations
Some results for conjugate equations
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DOI：
10.1007/s00010-018-0633-9
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发表时间：
2018-06
影响因子：
0.8
通讯作者：
K. Okamura
中科院分区：
文献类型：
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作者：
K. Okamura
本文研究了一类共轭方程，它是de Rham泛函方程的推广。给出了两种不同假设下解的存在唯一性的充分条件。我们考虑解的正则性。在我们的框架中，两个迭代函数系统与一系列共轭方程相关联。我们利用具有公共概率向量的两个迭代函数系统的不变测度来描述局部正则性。本文给出了二维标准Sierpiński垫片上的一类新的非调和函数或分形插值函数的分形函数，特别是一个存在无穷多个解的例子。我们还考虑了某种稳定性。
In this paper we consider a class of conjugate equations, which generalizes de Rham’s functional equations. We give sufficient conditions for the existence and uniqueness of solutions under two different series of assumptions. We consider regularity of solutions. In our framework, two iterated function systems are associated with a series of conjugate equations. We state local regularity by using the invariant measures of the two iterated function systems with a common probability vector. We give several examples, especially an example such that infinitely many solutions exists, and a new class of fractal functions on the two-dimensional standard Sierpiński gasket which are not harmonic functions or fractal interpolation functions. We also consider a certain kind of stability.