Fractional Powers of Anti-Triangular Operator Matrices and Their Applications
Year: 2025
Type: article
Abstract: The concept of fractional powers of operators was initially developed within the framework of functional analysis and has since played a significant role in the study of evolution equations, abstract differential equations, and complex dynamical systems. Meanwhile, the operator matrix approach has emerged as a powerful and widely used tool for analyzing the structural properties of operators. Motivated by these developments, this paper focuses on the explicit computation of fractional powers of anti-triangular operator matrices. Specifically, we first derive an explicit formula for the fractional powers of off-diagonal operator matrices by employing the formal determinant of block operator matrices. Then, based on the Schur factorization, we obtain a representation for the fractional powers of the general anti-triangular case. As applications, the obtained results are further applied to certain differential equations.
Source: Axioms
Authors: Lei Zhao, Yongqing Fu, Junjie Huang
Institutions: Inner Mongolia University, Ordos Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4416665292