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On the harmonic extension approach to fractional powers in Banach spaces
Fractional Calculus and Applied Analysis ( IF 3 ) Pub Date : 2020-08-26 , DOI: 10.1515/fca-2020-0055
Jan Meichsner 1 , Christian Seifert 1
Affiliation  

Abstract We show that fractional powers of general sectorial operators on Banach spaces can be obtained by the harmonic extension approach. Moreover, for the corresponding second order ordinary differential equation with incomplete data describing the harmonic extension we prove existence and uniqueness of a bounded solution (i.e., of the harmonic extension).

中文翻译:

Banach空间中分数幂的谐波可拓方法

摘要 我们表明,可以通过谐波扩展方法获得 Banach 空间上一般扇形算子的分数幂。此外,对于对应的具有描述调和扩展的不完整数据的二阶常微分方程,我们证明了有界解(即调和扩展的)的存在性和唯一性。
更新日期:2020-08-26
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