论文标题
关于谐波分析的注释第二部分：傅立叶系列
Notes on harmonic analysis Part II: the Fourier Series
论文作者
论文摘要
傅立叶系列是我们在谐波分析中介绍的第二本书。谐波分析是数学研究最迷人的领域之一。它在许多数学领域的发展中的中心地位，例如部分微分方程和整合理论及其在科学和工程领域中的许多多样化的应用，使其成为一个有吸引力的研究和研究领域。 这些笔记的目的是向数学，物理学或工程科学的学生介绍该主题的基本思想和定理。我们的目标是以最大的清晰和准确性来说明主题，学生或有兴趣的读者很容易理解。实际上，我们实际上提供了所有定理的完整证明。这种方法将阐明所采取的必要步骤和用于完成每个证明的机械。 理解所介绍的主题的先决条件是Lebesgue度量和积分不可或缺的知识。这将为高级本科生或数学研究生提供足够的数学背景。
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial differential equations and integration theory and its many and diverse applications in sciences and engineering fields makes it an attractive field of study and research. The purpose of these notes is to introduce the basic ideas and theorems of the subject to students of mathematics, physics, or engineering sciences. Our goal is to illustrate the topics with utmost clarity and accuracy, readily understandable by the students or interested readers. Rather than providing just the outlines or sketches of the proofs, we have actually provided the complete proofs of all theorems. This approach will illuminate the necessary steps taken and the machinery used to complete each proof. The prerequisite for understanding the topics presented is the knowledge of Lebesgue measure and integral. This will provide ample mathematical background for an advanced undergraduate or a graduate student in mathematics.
