Title: Theory of Differential Operators
Authors: Mohammed A. Akraa, Amera W. Al-funjan, Huda A.Hadi,
Volume: 9
Issue: 8
Pages: 104-105
Publication Date: 2025/08/28
Abstract:
The concept of differential operators between differentiable vector bundles is discussed in detail in this work. We define a differential operator as a local linear mapping and analyze its fundamental properties, such as local structure and order. This paper explains how differential operators can be locally represented by matrices of partial differential operators and introduces the concept of the principal symbol as a coordinate-independent linear operator. The idea of the transposed operator and its connection to the principal symbol are also explained in detail