标题： 范围递减群同态和加权复合算子 显示英文标题

标题： Range decreasing group homomorphisms and weighted composition operators

摘要： 我们提出了在李群丛的光滑截面空间之间的群同态成为加权复合算子的必要且充分条件。 这些结果为与加权复合算子相关的广泛问题提供了新的见解。 具体而言，我们证明了代数丛的光滑截面空间的代数结构，其中典型纤维是一个正维数的单无交换代数，完全决定了丛结构。 此外，我们推导了Shanks-Pursell定理的同态版本，并识别了有限维流形上光滑函数空间之间乘法半群的同态类，包括所有同构。 我们的方法基于一种称为范围递减群同态的方法。 显示英文摘要

摘要： We present necessary and sufficient conditions for a group homomorphism between spaces of smooth sections of Lie group bundles to be a weighted composition operator. These results provide new insights into a wide range of problems related to weighted composition operators. Specifically, we prove that the algebraic structure of the space of smooth sections of an algebra bundle, where the typical fiber is a positive dimensional simple unital algebra, completely determines the bundle structure. Furthermore, we derive a homomorphism version of the Shanks-Pursell theorem and identify a class of homomorphisms of multiplicative semigroups between spaces of smooth functions on finite dimensional manifolds, including all isomorphisms. Our approach is based on a method called range decreasing group homomorphisms.