这篇开创性研究通过将深度神经网络（DNN）视为输入变量与参数变量的二元函数，首次构建了基于再生核Banach空间（RKBS）的深度学习假设空间。作者证明了该空间的弱*闭包性质，并构造了显式再生核，为DNN学习模型（包括正则化学习和最小范数插值问题）建立 ...

Banach spaces, as complete normed vector spaces, have long served as a fundamental framework for analysing linear operators. Operator theory within these spaces investigates the properties and ...

The study of isometries within Banach spaces has emerged as a pivotal area of contemporary research, advancing both fundamental theory and practical applications. At its core, an isometry is a mapping ...

He was so quick, so strong, so tough they called him, "The Horse." Ed Banach didn't elude people, he slipped around them like he was oiled up, and they were a pillar of concrete. One second ...